Constraining Radio Mode Feedback in Galaxy Clusters with

DES 2019-0324FERMILAB PUB-19-204-AE

MNRAS 000, 000–000 (0000) Preprint 24 March 2020 Compiled using MNRAS LATEX style file v3.0

Constraining Radio Mode Feedback in Galaxy Clusterswith the Cluster Radio AGN Properties to z∼1

N. Gupta?1,2,3,4, M. Pannella2, J. J. Mohr2,3,4, M. Klein2,4, E. S. Rykoff5,6, J. Annis7, S. Avila8,F. Bianchini1, D. Brooks9, E. Buckley-Geer7, E. Bulbul10,11, A. Carnero Rosell12,13, M. Car-rasco Kind14,15, J. Carretero16, I. Chiu17, M. Costanzi2, L. N. da Costa13,18, J. De Vicente8,S. Desai19, J. P. Dietrich2,3, P. Doel9, S. Everett20, A. E. Evrard21,22, J. Garcıa-Bellido8,E. Gaztanaga23,24, D. Gruen25,5,6, R. A. Gruendl14,15, J. Gschwend13,18, G. Gutierrez7,D. L. Hollowood20, K. Honscheid26, D. J. James10, T. Jeltema20, K. Kuehn27, C. Lidman28,M. Lima29,13, M. A. G. Maia13,18, J. L. Marshall30, M. McDonald11, F. Menanteau14,15,R. Miquel31,16, R. L. C. Ogando13,18, A. Palmese,7, F. Paz-Chinchon14,15, A. A. Plazas32,C. L. Reichardt1, E. Sanchez8, B. Santiago33,13, A. Saro34,35,36, V. Scarpine7, R. Schindler6,M. Schubnell22, S. Serrano23,24, I. Sevilla-Noarbe8, X. Shao2, M. Smith37, J. P. Stott38,V. Strazzullo2, E. Suchyta39, M. E. C. Swanson15, V. Vikram40, and A. Zenteno41

The authors’ affiliations are shown in the end of manuscript.

Accepted ???. Received ???; in original form ???

ABSTRACTWe study the properties of the Sydney University Molonglo Sky Survey (SUMSS)843 MHz radio AGN population in galaxy clusters from two large catalogs createdusing the Dark Energy Survey (DES): ∼11,800 optically selected RM-Y3 and ∼1,000X-ray selected MARD-Y3 clusters. We show that cluster radio loud AGN are highlyconcentrated around cluster centers to z ∼ 1. We measure the halo occupation numberfor cluster radio AGN above a threshold luminosity, finding that the number of radioAGN per cluster increases with cluster halo mass as N ∝M1.2±0.1 (N ∝M0.68±0.34)for the RM-Y3 (MARD-Y3) sample. Together, these results indicate that radio modefeedback is favoured in more massive galaxy clusters. Using optical counterparts forthese sources, we demonstrate weak redshift evolution in the host broad band colorsand the radio luminosity at fixed host galaxy stellar mass. We use the redshift evolutionin radio luminosity to break the degeneracy between density and luminosity evolutionscenarios in the redshift trend of the radio AGN luminosity function (LF). The LFexhibits a redshift trend of the form (1 + z)γ in density and luminosity, respectively,of γD = 3.0± 0.4 and γP = 0.21± 0.15 in the RM-Y3 sample, and γD = 2.6± 0.7 andγP = 0.31±0.15 in MARD-Y3. We discuss the physical drivers of radio mode feedbackin cluster AGN, and we use the cluster radio galaxy LF to estimate the average radio-mode feedback energy as a function of cluster mass and redshift and compare it to thecore (< 0.1R500) X-ray radiative losses for clusters at z < 1.

Key words: galaxies: clusters: general; galaxies: active; galaxies: luminosity function,mass function; submillimeter: galaxies; cosmology: observations

1 INTRODUCTION

A number of studies of low redshift clusters have shownthat local instabilities due to active galactic nuclei (AGN)outbursts reheat the intracluster medium (ICM) and reg-ulate the cooling in the cluster centre through radio-mode

? [email protected]

AGN feedback (e.g. McNamara et al. 2005; Rafferty et al.2006; Blanton et al. 2010; Ogrean et al. 2010; Ehlert et al.2011; Bırzan et al. 2012; Gitti et al. 2012; Bharadwaj et al.2014; Voit et al. 2015; ?). There is some evidence of theevolution of AGN feedback in massive field galaxies up toz ∼ 1.3 (Simpson et al. 2013), suggesting that the balancebetween radiative cooling and AGN feedback was achievedin the early universe. However, the evolution of AGN feed-

c© 0000 The Authors

arX

iv:1

906.

1138

8v2

[as

tro-

ph.G

A]

23

Mar

202

0

2 N. Gupta, M. Pannella, J. J. Mohr, et al.

back in galaxy clusters with redshift and mass is not wellstudied. Hlavacek-Larrondo et al. (2013) studied X-ray AGNemission in brightest cluster galaxies (BCGs) up to z=0.6,showing that the typical nuclear AGN X-ray luminosity in-creases by a factor of 10, mostly due to an increase in thefraction of BCGs hosting X-ray AGN between z = 0.1 andz = 0.6. Bırzan et al. (2017) studied 21 Sunyaev-Zel’dovichEffect (SZE; Sunyaev & Zel’dovich 1972) selected clusterswith 0.3 < z < 1.3 and found higher radio luminosity ascompared to X-ray luminosity at higher redshifts (z > 0.6),presumably due to increased merging activity of galaxy clus-ters that may trigger the radio mode feedback. ? com-piled an X-ray luminous BCG sample in the redshift ranges0.2 < z < 0.3 and 0.55 < z < 0.75, and contrastingly foundno evidence for evolution. These results should however beconsidered as preliminary, because the BCG sample is sim-ply collected from all publicly available observations of clus-ters and groups, and so the sample selection is not well un-derstood.

Previous studies of cluster radio sources have either notconsidered the redshift trends in the cluster radio sourceproperties (e.g. Lin & Mohr 2007; Lin et al. 2009; Sehgalet al. 2010; Lin et al. 2015) or have shown contrasting trends(e.g. Sommer et al. 2011; Bırzan et al. 2017; Lin et al. 2017;Gupta et al. 2017, hereafter G17) due to statistical limita-tions of galaxy cluster samples extending to higher redshift.Moreover, given the relatively featureless shape of the radiogalaxy luminosity function (LF, for e.g. G17), it is typicallynot possible to differentiate a change in number density froma change in the typical AGN luminosity (so-called luminos-ity evolution). Typically, the reported redshift trends in theproperties of cluster radio sources have been presented as ei-ther pure density or pure luminosity evolution (e.g. Sommeret al. (2011)).

In this paper, we present the redshift and mass trendsof the properties of cluster radio sources. The sources weconsider come from the 843 MHz Sydney University Mo-longlo Sky Survey (SUMSS; Bock et al. 1999; Mauch et al.2003; Murphy et al. 2007) radio source catalog, and at thedistances where we study these sources they correspond tohigh radio luminosity objects that are dominated by AGNsynchrotron emission. We study the cluster radio AGN tomeasure their spatial distribution in clusters, the halo occu-pation number (HON) or characteristic number within thecluster virial region, the radio luminosity evolution at fixedstellar mass and the luminosity functions. This study uses alarge ensemble of optically and X-ray selected galaxy clus-ters that have been constructed using the first three yearsof data from the Dark Energy Survey (DES-Y3; see Ab-bott et al. 2018, for discussion of the data release) and theROSAT All Sky Survey 2RXS faint source catalog (RASS;Boller et al. 2016).

Our study primarily employs statistical backgroundsubtraction to correct for those radio AGN that are notphysically associated with the clusters. However, we alsouse DES-Y3 survey data to identify the optical counter-parts of cluster radio AGN and to directly select those AGNwhose redshifts are consistent with the cluster redshifts.This also allows us to perform Spectral Energy Distribu-tion (SED) analyses of these radio source counterparts toobtain constraints on the stellar mass and spectral type ofthese sources. This information then allows us to probe the

relationship between stellar mass and radio luminosity forradio AGN, which provides direct constraints on the redshiftevolution of cluster radio AGN. We use this information to-gether with the LF to jointly constrain number density andluminosity evolution for the cluster radio AGN population.With measurements of the radio AGN LF and its depen-dence on cluster mass and redshift, we then estimate massand redshift trends in the radio mode feedback and its rela-tionship to the X-ray radiative losses within cluster cores.

The plan of the paper is as follows: In Section 2, wediscuss the observations and the data used in this work. Wedescribe the SED analysis and the cross-matching of radio tooptical sources in Section 2.4. Section 3 is dedicated to thestudies of surface density profiles, luminosity evolution, halooccupation numbers and LFs. Section 4 contains a discus-sion of the implications of our measured mass and redshifttrends for the physical drivers of radio mode feedback andthe balance of AGN feedback and X-ray radiative losses inthe cluster cores. We summarize our results in Section 5.Throughout this paper we assume a flat ΛCDM cosmologywith matter density parameter ΩM = 0.3 and Hubble con-stant H0 = 70 km s−1 Mpc−1. We take the normalizationof the matter power spectrum to be σ8 = 0.83.

2 DATA

We study the overdensity of radio point sources towardX-ray and optically selected galaxy clusters selected usingRASS and DES-Y3 observations. We focus on high luminos-ity radio AGN log [P/(W Hz−1)]> 23 that are selected fromthe SUMSS catalog observed at 843 MHz. A part of ouranalysis is supported through the identification of the opti-cal counterparts of these sources using the DES-Y3 obser-vations (see Section 3.2), but the rest of our results employstatistical background subtraction.

2.1 SUMSS catalog

The Sydney University Molonglo Sky Survey (SUMSS; Bocket al. 1999; Mauch et al. 2003; Murphy et al. 2007) imagedthe southern radio sky at 843 MHz with a characteristic an-gular resolution of ∼ 45′′ using the Molonglo ObservatorySynthesis Telescope (MOST, Mills 1981; Robertson 1991).The survey was completed in early 2007 and covers 8,100deg2 of sky with δ≤−30 and |b|≥10. The catalog contains210,412 radio sources to a limiting peak brightness of 6 mJybeam−1 at δ≤−50 and 10 mJy beam−1 at δ>−50. Atthe SUMSS selection frequency, we expect nearly all sourcesabove the flux selection threshold to be synchrotron dom-inated (de Zotti et al. 2005). The positional uncertaintiesgiven in the catalogue are a combination of fitting uncer-tainties and calibration uncertainties of the MOST and forsources with peak brightness A843 ≥20 mJy beam−1, theaccuracy is in the range 1′′ to 2′′ (see section 5.1 of Murphyet al. 2007). The flux measurements are accurate to within3 percent. The catalog is complete to 8 mJy at δ≤−50

and to 18 mJy at δ>−50, and we restrict our analysis tothese complete subsamples. At the SUMSS frequency, ap-proximately 10 percent of the sources exhibit extent alongone axis (Mauch et al. 2003).

MNRAS 000, 000–000 (0000)

Cluster Radio AGN to z∼1 3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0z

0

500

1000

1500

2000

Cou

nt

0

50

100

150

200RM-Y3MARD-Y3

14.0 14.5 15.0 15.5log(M200c) [M]

0

500

1000

1500

2000

2500

3000

3500

Cou

nt

0

50

100

150

200

250RM-Y3MARD-Y3

Figure 1. Distribution of RM-Y3 and MARD-Y3 galaxy clusters

as a function of redshift (upper panel) and mass (lower panel).Red bars show optically selected RM-Y3 clusters with median

mass and redshift of 1.52× 1014 M and 0.47, respectively. Bluebars show X-ray selected MARD-Y3 clusters with median mass

and redshift of 5.06× 1014 M and 0.28, respectively. The color-coded vertical axes labels on the left and right sides of the plotsrepresent the number of clusters in the RM-Y3 and MARD-Y3catalogs, respectively.

2.2 DES-Y3 data

We make use of the DES Y3 GOLD-release multiwalengthcatalog in its version 2.2, which covers ∼ 5000 deg2 ofthe southern celestial hemisphere and has about 60 per-cent overlap (∼ 3000 deg2) with the SUMSS survey. TheGOLD catalog is intended to be the basis for cosmologyanalyses with the Dark Energy Survey data. The GOLDcatalog consists of a validated object catalog with a set ofquality control flags and additional auxiliary data such asphotometric redshift information based both on neural net-works and Bayesian template fitting. Specifically, for eachobject in the DES catalog we make use of total magnitudes

with relative uncertainties (MAG AUTO from SExtractor;Bertin & Arnouts 1996) in the grizy bands and DES derivedphotometric redshifts (DNF MEAN) alongside further in-formation present in the catalog such as that derived fromSPREAD MODEL, which allows for object star–galaxy clas-sification (Desai et al. 2012), flagging of bad areas or bandspecific photometric measurement issues (for additional de-tails on the catalogs, see discussion in Morganson et al. 2018;Abbott et al. 2018).

2.3 Galaxy Cluster Catalogs

For this analysis we adopt the RM-Y3 catalog of 19,795 opti-cally selected clusters and the MARD-Y3 catalog of 2,171 X-ray selected clusters. The two cluster samples are describedbriefly in the following subsections.

2.3.1 Optically selected RM-Y3 catalog

We use optically selected galaxy clusters identified with thered-sequence Matched-filter Probabilistic Percolation algo-rithm (redMaPPer; Rykoff et al. 2014) from the Dark En-ergy Survey first three years of data (RM-Y3). As the namesuggests, redMaPPer (RM) can be used to identify clustersas over-densities of red-sequence galaxies. Precisely, the al-gorithm estimates the probability (Pmem) of a red galaxy tobe a cluster member given as

Pmem =λu(x)

λu(x) + bgal, (1)

where x is a vector that describes the observable propertiesof a galaxy (e.g., multiple galaxy colors, i-band magnitude,and position), u(x) is the density profile of cluster normal-ized to unity, bgal is the density of background galaxies andthe richness (λ) is estimated by summing up the member-ship probabilities of galaxies in the cluster region satisfyingthe constraint equation. RM has been shown to provide ex-cellent photometric redshifts as well as richness estimates.For instance, the catalogs have been shown to have highcompleteness and purity (Rozo & Rykoff 2014; Rozo et al.2014a,b) when the RM algorithm is applied to the Sloan Dig-ital Sky Survey (SDSS) Stripe 82 data (Annis et al. 2014),to the eighth SDSS data release (DR8 Aihara et al. 2011)and to the DES-Y1 and science verification (DES-SV) data(Rykoff et al. 2016; Soergel et al. 2016).

The RM-Y3 catalog (Rykoff et al., in prep) adopts abrighter luminosity threshold of 0.4 L∗ rather than the min-imum scatter luminosity threshold of 0.2 L∗ (Rykoff et al.2012) to get a clean sample of clusters above a richnessthreshold. The center of the cluster is taken to be theposition of the brightest cluster galaxy (BCG). There are19,795 galaxy clusters with λ ≥ 20 in the redshift range of0.1≤ z ≤0.8 with a median redshift of 0.47.

To estimate masses from the measured richnesses, weadopt an externally calibrated λ–mass relation. As discussedelsewhere (e.g. Capasso et al. 2019b), the λ–mass relation forSZE (Saro et al. 2015) and X-ray (Capasso et al. 2019b) se-lected cluster samples differs from that of optically selectedRM clusters (McClintock et al. 2019). The SZE analysis re-lies on SPT derived cluster masses, which have been shownto be consistent with those derived through weak lensinganalyses (Dietrich et al. 2019; Stern et al. 2019; Bocquet

MNRAS 000, 000–000 (0000)


et al. 2019). The X-ray analysis relies on masses derivedthrough a dynamical analysis whose systematics have beenstudied with simulations (Mamon et al. 2013) and throughcross-comparisons of weak lensing and dynamical masses(Capasso et al. 2019a). One clear difference is that the RMsample analysis relies on stacked weak lensing information,measuring the mean mass within bins of richness and red-shift, whereas the other studies mentioned infer the underly-ing mass-observable relation using scatter in the observableat fixed mass and applying corrections for the Eddingtonbias. However, the scale of the Eddington bias correction istoo small to explain the differences, and thus it may be thatthe differences are driven by residual contamination in theoptically selected RM sample that is not present in the SZEand X-ray selected samples.

Further study is warranted, but because we are em-ploying an optically selected RM sample to study the radiogalaxy population, we adopt the McClintock et al. (2019)calibration here when computing cluster masses,

M200m = Aλ

(λ

λP

)Bλ(

1 + z

1 + zP

)γλ, (2)

with Aλ = (3.08±0.15)×1014, Bλ = 1.356±0.052 and γλ =−0.30± 0.31. The pivot richness (λP) and redshift (zP) aregiven as 40 and 0.35, respectively. We further correct fromM200m to M200c using a model of the concentration-massrelation (Diemer & Kravtsov 2015), where M200m and M200c

are defined as the masses of the cluster within a sphere wherethe mean density is 200 times the mean and the criticaldensity of the Universe, respectively.

For the RM-Y3 sample, we find that M200c is in therange of 9.61× 1013 to 2.62× 1015 M with a median valueof 1.52× 1014 M. There are ∼11,800 clusters within 0.1 <z < 0.8 in the SUMSS region. Fig. 1 shows the mass andredshift distributions of the clusters.

2.3.2 X-ray selected MARD-Y3 catalog

We use the X-ray selected RASS cluster catalog confirmedand de-contaminated with the multi-component matchedfilter (MCMF) applied to DES-Y3 data to compare withradio source properties in RM-Y3 clusters. This X-ray se-lected cluster catalog (MARD-Y3; Klein et al. 2019) containsgalaxy clusters confirmed using a multi-component matchedfilter (Klein et al. 2018, MCMF) follow up in 5,000 deg2 ofthe DES-Y3 optical data of the ∼ 20, 000 sources from thesecond ROSAT All-Sky Survey source catalog (2RXS) pre-sented in Boller et al. (2016). The MCMF tool is designed foruse on large scale imaging surveys such as the DES to do au-tomated confirmation, redshift estimation and suppressionof random superpositions of X-ray/ SZE cluster candidatesand physically unassociated optical systems. MCMF is usedto identify optical counterparts as peaks in galaxy richnessas a function of redshift along the line of sight toward each2RXS source within a search region informed by an X-rayprior. All peaks are assigned a probability fcont of being arandom superposition and fcont is extracted from the galaxyrichness distributions along large numbers of random linesof sight. In this work, we present radio properties using acatalog with fcont < 0.2 containing 2,171 galaxy clusters.The catalog covers a redshift range of 0.02 < z < 1.1 with

more than 100 clusters at z > 0.5, and it has residual con-tamination of 9.6 percent.

The X-ray luminosity of clusters in the catalog is esti-mated from the source count rate in the 0.1-2.4 keV bandwithin a 5′ aperture radius around each 2RXS source. Thissimplified luminosity LX has been shown to be simply re-lated to L500c, the luminosity within a radius within whichthe mean density is 500 times the critical density of theuniverse at the assumed cluster redshift (Klein et al. 2019).The mass in the catalog is derived using the estimated lu-minosity at that redshift and an LX–mass scaling relationfrom the analysis of Bulbul et al. (2019), which uses SZEbased mass constraints from the cosmological analysis of theSPT-SZ cluster sample (de Haan et al. 2016) together withdeep XMM-Newton observations of a subset of those clustersto consistently derive multiple observable to mass relations.These SPT-SZ masses have since been shown to be consis-tent with weak lensing (Dietrich et al. 2019; Stern et al.2019; Bocquet et al. 2019) and dynamical masses (Capassoet al. 2019a). The scaling relation has the following form

LX = AX

(M500c

Mpiv

)BX(

E(z)

E(zpiv)

)(1 + z

1 + zpiv

)γX. (3)

Here, AX, BX and γX are the parameters with best fit valuesof 4.15+1.10

−0.81 × 1044 erg s−1, 1.91+0.18−0.15 and 0.20+0.41

−0.43, respec-tively (Bulbul et al. 2019, table 5 solution II for LX,cin).The pivot mass Mpiv and redshift zpiv are 6.35 × 1014 Mand 0.45, respectively. The function E(z) ≡ H(z)/H0

which gives the ratio between the Hubble parameter andits present-day value, and M500c is defined as the mass ofthe cluster within a sphere where the mean density is 500times the critical density of the Universe. We account for Ed-dington bias following the description in Mortonson et al.(2011) and using log-normal scatter in the LX-mass rela-tion σln X = 0.25+0.08

−0.13 (Bulbul et al. 2019). Further, wecorrect from M500c to M200c again using a model of theconcentration-mass relation (Diemer & Kravtsov 2015).

The median mass and redshift of the MARD-Y3 sampleare 5.06× 1014 M and 0.28, respectively, and the distribu-tions are shown in Fig 1. A mass versus redshift plot for theMARD-Y3 sample is presented in Klein et al. (2019, figure9 grey and black circles). Approximately 1,000 MARD-Y3clusters between 0.1 < z < 0.8 lie within the SUMSS regionand are used for this analysis. This sample is significantlysmaller than the RM-Y3 sample, however, the unique massand redshift range as well as the selection of MARD-Y3 sam-ple in X-ray band provides an interesting complement to theRM-Y3 sample.

The cluster centers in the MARD-Y3 catalog are iden-tified from optical data (see section 3.9; Klein et al. 2019)as the position of the rBCG, the brightest galaxy within1.5 Mpc of the X–ray centroid that has all colors within 3-σof red sequence at the redshift of cluster, as long as that po-sition is within 1′ of the peak of the red galaxy distributionof the cluster. If the rBCG is too offset from the red galaxypopulation, the cluster center is defined to be that of the redgalaxy population.

2.4 Optical counterpart identification

Our core analysis focuses on the statistical overdensity ofradio AGN toward galaxy clusters to constrain the proper-

MNRAS 000, 000–000 (0000)


Figure 2. The surface number density of DES galaxies (left) as a function of the offset from SUMSS radio AGN (solid lines) for different

stellar mass ranges. The peak at small offset is produced by physically associated sources, and the decline to a flatter distribution atlarger radius is caused by physically unassociated sources. Dotted lines show the level of the flat surface density from non–physical cross-

matches for the different stellar mass bins. These surface densities are used to estimate contamination and completeness as a function of

stellar mass for the cross–matched sample. High mass galaxies are much more likely to be physical counterparts of the radio AGN (seeSection 2.4). Comparison between redMaPPer cluster redshifts and the photometric redshifts of SUMSS counterparts of DES galaxies

used in this work (right). The solid red line is the bisector, while the dotted lines show the 2% (±1σ) and 6% (±3σ) bands. These lattervalues are estimated as the normalized median absolute deviation (NMAD) of the |∆z|/(1 + z) distribution. Optical counterparts (green

points) are assigned to the cluster if their DES photo-z deviates from that of the cluster by less than ∆zphot = 0.06(1 + z), i.e., three

times the NMAD.

ties of cluster radio AGN. However, this analysis is comple-mented by an analysis of a subset of radio AGN whose opti-cal counterparts we have identified in the DES-Y3 dataset.Here we describe the counterpart identification and stellarmass estimation needed to undertake that analysis.

A complete description of the derivation and accuracyof galaxy stellar masses as well as the cross-matching tech-nique used to uniquely associate a DES counterpart to eachSUMSS radio source will be provided in a forthcoming work(Pannella et al., in prep.). Here, we briefly summarize themain steps of our procedure: 1) for each radio source abovethe nominal SUMSS survey completeness limit in radio fluxdensity, we select all DES catalog entries lying within 20′′; 2)the catalog of plausible DES counterparts is trimmed downby applying a cut in imag < 23 AB magnitudes, and byremoving unresolved sources from the catalog by imposingthat the EXTEND CLASS flag is greater than 0, and, fi-nally, by removing all galaxies for which the DES photo-metric redshift was not constrained.

We derive stellar masses for all the objects in our samplewith fastpp1 (a C++ version of the SED fitting code FAST;Kriek et al. 2009) on the grizY total magnitudes. We useBruzual & Charlot (2003) with delayed exponentially declin-ing star formation histories (SFHs, ψ(t) ∝ t

τ2exp(−t/τ))

with 0.01< τ <10 Gyr, solar metallicities (Z = 0.02),the Salpeter initial mass function (Salpeter 1955), and the

1 Publicly available at https:// github.com/cschreib/fastpp

Calzetti et al. (2000) reddening law with a range of extinc-tion AV up to 4 magnitudes.

We then examine the surface density on the sky of DESsources as a function of their distance from the SUMSS ra-dio AGN for different bins of stellar mass. This is shown inthe left panel of Fig. 2 with solid lines in six different col-ors, corresponding to different ranges of stellar mass. Thesesurface density profiles exhibit a peak at small separation,which corresponds to actual physical counterparts droppingaway to a flat surface density that corresponds to a regiondominated by physically unassociated galaxies projected atrandom near the radio AGN. It is evident that for higherstellar mass the central peak has a higher contrast with re-spect to the flat background, which is an indication that forthese stellar mass ranges a larger fraction of galaxies cor-respond to physical counterparts of the radio AGN. Thisis not surprising, because AGN powered radio sources aretypically hosted by passive, massive and bulge-dominatedgalaxies (Best et al. 2007; Lin & Mohr 2007; Kauffmannet al. 2008; Lin et al. 2010; Best & Heckman 2012).

By fitting for the level of the flat surface density fromrandom (i.e., non–physical) cross-matches (see dotted linesin the left panel of Fig. 2), we can then estimate for anygiven matching radius the resulting contamination of thesample. In addition, we can integrate over the portion of thecentral peak extending beyond the matching radius to esti-mate the incompleteness within each mass bin for a givenmatching radius. For the purposes of this analysis, we adopta simple matching criteria that produces a sample with no

MNRAS 000, 000–000 (0000)


more than 15 percent contamination. Practically, this meansthat we define the cross–matched host for each radio AGNto be the nearest DES galaxy with i < 23.0 that has stel-lar mass in one of the top two bins (logM∗ > 11.3 and11.3 > logM∗ > 10.9), within a maximum offset distance of10′′ or 6′′, respectively. Within the lower mass bins it is notpossible to define a sensible maximum offset distance wherethe contamination is as low as 15 percent. The estimatedcompleteness of this cross–matched sample is ∼60 percent.

This host identification procedure produces a catalog of24,998 unique associations of SUMSS detected radio AGN toa DES galaxy host. In this work we specifically concentrateon the 2,264 candidate cluster radio AGN that lie withinthe radius θ200 of a RM-Y3 cluster. Among this latter sub-sample, only 1,643 (73 percent) have photometric redshiftsthat place them within a cluster (see the right panel ofFig. 2). To assign cluster membership to the radio AGN,we compare the DES photometric redshift (DNF MEAN)of each source to the redshift of the RM-Y3 cluster. If asource deviates from the cluster redshift by less than 3times the normalized median absolute deviation (NMAD)(δz = ∆z/(1 + z) = 0.02), we consider it to be a clustermember and therefore a confirmed cluster radio AGN. Wedo not carry out separate cross-matching in the MARD-Y3sample, because the sample is an order of magnitude smallerthan the RM-Y3 sample.

3 CLUSTER RADIO AGN PROPERTIES

We present measurements of the radial distribution of AGNaround clusters in Section 3.1, and present new constraintson the radio luminosity and color evolution of radio AGNusing the sample of matched optical counterparts in Sec-tion 3.2. Leveraging these results, we then present the clus-ter radio AGN luminosity function in Section 3.3 and thehalo occupation number in Section 3.4.

3.1 Radial distribution

We study the radial distribution of radio AGN in the clusterθ200c region by stacking the flux limited and complete sam-ples of radio AGN overlapping the RM-Y3 and MARD-Y3samples. To do this we adopt the optical centers for bothsamples, described in detail in separate references (Rykoffet al. 2014; Klein et al. 2019).

Following G17, we use the projected NFW profile Σ(x)(Navarro et al. 1997; Bartelmann 1996) as a fitting functionfor the radial distribution. Here x = r/rs and rs = R200c/c,where c is the concentration parameter and x is equivalentto c for r = R200c. The total surface density of the radioAGN (ΣT) as a function of x around the cluster has bothcluster and background components (ΣB) and is written as

ΣT(x) = Σ(x) + ΣB, (4)

and to reduce the covariance between the central amplitudeand concentration, we write this in terms of the total numberof galaxies in the cluster sample as

ΣNT(x) = ΣN(x) + ΣBA, (5)

where A is the solid angle of the annulus or bin and the totalnumber of background subtracted galaxies ΣN(x) = ΣN200

10−2 10−1 100 101

θ/θ200

100

101

102

103

ΣT

/Σ

B

RM-Y30.1 < z < 0.25

0.25 < z < 0.5

0.5 < z < 0.78

MARD-Y3

Figure 3. The projected radial distribution of radio AGN ob-

served at 843 MHz around the centers of the optically selectedRM-Y3 (gray) and X-ray selected MARD-Y3 (blue) galaxy clus-

ters. The best fit projected NFW models are also shown as solid

lines in gray and blue with the model parameters listed in Table 1.The fits are evaluated using much smaller bins (∼ 0.001 θ/θ200)

in comparison to the data points shown here, which use larger

bins to reduce Poisson noise for the figure. We also show the bestfit NFW models in three redshift bins using the RM-Y3 catalog

represented by dashed lines. We see a decrease in concentration ofradio sources in clusters with increasing redshift for both RM-Y3

and MARD-Y3 selected cluster samples (see Table 1).

for r = R200c. We fit our stacked distribution of radio AGNto a model with three parameters: c, ΣN200 and ΣB (seeG17). We stack radio AGN out to 10 × θ200c to allow for agood constraint on the effective background density ΣB. Werefer to ΣB as the effective background density, because ourstacks are constructed using sources down to the flux limit ofthe SUMSS survey, and as described in Section 2.1 this fluxlimit has two different values, depending on the declinationof the cluster.

In the fit we employ the Cash (1979) statistic

C =∑i

(ΣNd

T,i ln(ΣNmT,i)− ΣNm

T,i − ΣNdT,i ln(ΣNd

T,i)

+ΣNdT,i,

),

(6)

where ΣNmT,i is the total number of galaxies from the model

as in equation (5) and ΣNdT,i is the total number of galax-

ies in the observed data in the ith angular bin. We usethe Markov Chain Monte Carlo (MCMC) code, emcee (aPython implementation of an affine invariant ensemble sam-pler; Foreman-Mackey et al. 2013) to fit the model to thedata throughout this work. In the fitting we adopt a binsize corresponding to θ200c/1000 and fit over the region ex-tending to 10θ200c. The concentration parameter is sampledin log space during the fit and the profile is centrally con-centrated with c = 143+10

−9 and 144+30−25 for the RM-Y3 and

MARD-Y3 cluster samples, respectively.We use this model of the radial distribution of radio

AGN in the next section to correct the projected LF to the

MNRAS 000, 000–000 (0000)


Table 1. Best fit projected NFW model parameters for the ra-dial distribution of a complete sample of radio AGN observed

at 843 MHz in a stack of optically selected RM-Y3 and X-ray se-

lected MARD-Y3 galaxy clusters. The best fit parameters are alsoshown for subsets of these clusters in three redshift bins where for

each we present concentration c, the estimate of the total number

of radio AGN within R200c in our sample ΣN200 and the effectivebackground surface density of radio AGN ΣB.

Cluster sample c ΣN200 ΣB [deg−2]

RM-Y3 (all) 143+11−10 2198+55

−53. 20.23± 0.05

0.1 < z < 0.25 203+35−29 553+27

−26 20.33± 0.11

0.25 < z < 0.5 140+16−15 1068+36

−37 20.00± 0.12

0.5 < z < 0.8 105+16−13 583+27

−26 20.51± 0.20

MARD-Y3 (all) 144+30−25 425+30

−29 19.89± 0.12

0.1 < z < 0.25 193+60−28 221+18

−17 19.91± 0.15

0.25 < z < 0.5 120+40−28 160+15

−14 19.62± 0.24

0.5 < z < 0.8 100+58−40 48+08

−07 21.20± 0.68

LF within the cluster virial region defined by R200c (follow-ing Lin et al. 2004). We measure the surface density profilesby dividing RM-Y3 and MARD-Y3 catalogs in three red-shift bins and see a clear tendency for higher concentrationat lower redshifts in both catalogs. The best fit NFW pa-rameters are presented in Table 1. We use the flux limitedsample rather than a luminosity limited sample for this mea-surement because of the larger number of available systems.This does not affect the trends in concentration seen here.

We test the reliability of trends in concentration for mis-centring in the RM-Y3 sample. We select clusters for whichthe probability that each of the alternate cluster centres isthe correct centre Pcen > 0.95 (Rykoff et al. 2014). We findthat this sub-sample of clusters show similar concentrationtrends with c = 250+40

−35, 141+21−18 and 107+18

−16 for low to highredshift bin in Table 1.

High central concentrations of radio sources in galaxyclusters have been observed in previous studies. Lin & Mohr(2007) studied radial distribution of cluster radio AGN ob-served at 1.4 GHz with P > 1023 W Hz−1 in a sample of X-ray selected galaxy clusters with z < 0.2, finding c = 52+24

−14.G17 studied radial profiles of cluster radio AGN at 150 GHzin the Meta-Catalog of X-ray detected Clusters of galax-ies (MCXC) with median z = 0.1 and found c ∼ 100. Theresults presented here indicate that centrally concentratedcluster radio AGN are present over a broad range of clustermass M200c > 1× 1014 and out to redshift z ∼ 0.8.

In Fig. 3 we show the best fit surface density profiles anddata. To create these plots we combine many bins to reducethe noise in the measured radial profiles. Following G17,we normalize the vertical axes of this plot with the meannumber density of background sources (ΣB). Fig. 3 showsthat ΣB is a good estimation of the background numberdensity of the clusters, as ΣT/ΣB is consistent with 1 outsidethe cluster.

3.2 Host properties of the cross–matched sample

In the RM-Y3 cluster sample there are 1,643 cluster ra-dio AGN with identified optical counterparts. This cross–matched sample has an estimated contamination of 15 per-cent and an estimated completeness of 60 percent (see Sec-tion 2.4). Of the 11,800 RM-Y3 clusters lying within theSUMSS region, 1,579 (13 percent) host at least one con-firmed cluster radio AGN associated with the cluster byits redshift. The vast majority of these (95 percent) con-tain a single cluster radio AGN, 87 contain two radio AGN,one cluster contains three and one other contains four radioAGN all consistent with their cluster redshift. Finally, 1,044(63 percent) of the total sample of 1,643 cross–matched AGNare projected to lie within 0.1r200, consistent with the cen-trally concentrated radial profile for the statistically definedcomplete sample in Section 3.1.

In the subsections below we describe the radio powerto stellar mass relation of this sample (Section 3.2.1) andthen examine the typical broad band colors as a function ofredshift (Section 3.2.2).

3.2.1 Radio luminosity evolution at fixed host mass

To constrain the evolution of the radio luminosity withredshift at fixed stellar mass, we use the ensemble ofSUMSS sources with DES-Y3 counterparts. In particular,we take the high luminosity sample of radio sources withlog [P/(W Hz−1)] > 25.3 in the whole redshift range of DES-Y3 RM clusters, corresponding to 510 cluster radio AGN.This choice of luminosity cut is justified in Fig. 4, where weshow the relation between the 843 MHz luminosity and theredshift of radio AGN. Above this luminosity cut, we have asample of sources that can be studied over the full redshiftrange of our cluster samples, whereas if we were to push tolower radio luminosities we would only expect to find thosesources in our flux limited sample over a narrower range oflower redshifts.

We fit a power law relation of the following form toconstrain a relation between 843 MHz radio power (P843MHz,calculated using the redshift of each radio source) and thestellar mass (M∗) of radio sources obtained from the SEDfitting analysis described in Section 2.4

P843MHz = 10APM

(M∗

M∗,piv

)BPM(

1 + z

1 + zpiv

)γPM

, (7)

where M∗,piv = 3.7 × 1011 M and zpiv = 0.51 are the me-dian stellar mass and redshift of the subsample. The bestfit parameters are APM = 25.51± 0.006, BPM = 0.01± 0.02and γPM = 0.30 ± 0.15. Along with these parameters wealso vary the log normal scatter in radio luminosity atfixed stellar mass in the relation, finding a best fit valueσlogP = 0.31± 0.01.

These results make it clear that, unlike X-ray AGN,cluster high power radio AGN exhibit no correlation (BPM =0.01± 0.02) between their radio luminosity and their stellarmass (which is a predictor of the underlying supermassiveblack hole mass) at all redshifts probed by our sample. Thischaracteristic of radio mode feedback has previously beennoted (Best et al. 2007; Lin & Mohr 2007).

The relation has a scatter of ∆ log10 P = 0.31 ± 0.01,and the population we are studying exhibits a weak trend

MNRAS 000, 000–000 (0000)


Figure 4. Luminosity distribution of SUMSS sources (left) observed at 843 MHz as a function of redshift. The redshifts are obtained by

cross matching SUMSS with the DES-Y3 catalogs. The black points show radio sources inside θ200 of RM clusters, the red squares show

instead the radio sources identified as cluster members. The vertical dotted lines represent the three redshift bins used in this work, whilethe solid horizontal lines show the luminosity completeness levels at different redshifts. Distribution of SUMSS detected cluster members

(right) in radio luminosity and stellar mass, color coded by redshift (redshift ranges labeled). Empty squares show median luminosities

in bins of stellar mass and redshift over a luminosity range where completeness is assured at all redshifts, log P843MHz > 25.3, see leftpanel. Our results are consistent with a modest increase in the luminosity of cluster radio AGN at fixed stellar mass over the explored

redshift range (see Section 3.2.1).

for the radio luminosity at fixed stellar mass to increase withredshift γPM = 0.30±0.15. Along with this weak luminosityevolution with redshift, it has been noted that the mechan-ical feedback in comparison to the radio luminosity is alsoapproximately constant with redshift to z ∼ 0.6 (Hlavacek-Larrondo et al. 2012). This provides an indication that indi-vidual radio galaxies are only moderately more radio lumi-nous at high redshift and that the feedback events drivingradio emission and radio mode feedback are not changingdramatically with redshift. We will use this new constrainton cluster radio AGN evolution to disentangle density evo-lution and luminosity evolution in the cluster radio AGNluminosity function in Section 3.3.

3.2.2 SED evolution

Broad band colors constrain the SED of the cluster radioAGN hosts and provide insights into the presence of ongoingstar formation or optical AGN emission. In Fig. 5 we plotthe broad band color offsets of the radio AGN hosts from themean red sequence (RS) color as a function of redshift. TheRS colors are defined using a sample of ∼103 clusters withspectroscopic redshifts studied within DES as part of thecalibration of an optical counterpart and redshift estimationcode called MCMF (Klein et al. 2018, 2019). Because theRS color model makes use of single object fitting (SOF)magnitudes present in the DES catalog (see Klein et al. 2019and references therein for more details), for this purpose weuse the SOF magnitudes for the SUMSS source counterparts.

It is apparent that the hosts of radio AGN tend to haveintegrated colors very close to the RS at all redshifts. Thisis consistent with the established picture that radio AGN

Figure 5. Broad band color offsets from the red sequence as a

function of redshift for the cross–matched hosts of the SUMSScluster radio AGN. At all redshifts the host population has colorsvery similar to typical red sequence galaxies. Furthermore, there

is no obvious evidence for an evolution of median rest-frame col-ors with redshift (see discussion in Section 3.2.2). Overplotted as

boxes are the median color offsets of the hosts within redshiftbins.

are mostly hosted in massive galaxies with very little or noongoing star formation over the explored redshift range.

The redshift evolution of observed colors does not sug-gest any clear change in the stellar population propertiesof the host galaxies over time. When comparing rest-frame

MNRAS 000, 000–000 (0000)


Table 2. The best fit LF parameters for different samples ofcluster radio AGN. γD and γP are defined as the density and

luminosity redshift evolution parameters, respectively. The joint

constraints on γD and γP are obtained when a Gaussian prior onγP is adopted from the best fit redshift evolution of the stellar

mass - luminosity relation.

y x γD γP

RM-Y3

25.82± 0.04 26.56± 0.06 3.16± 0.43 −25.82± 0.04 26.56± 0.06 − 3.16± 0.42

25.75± 0.04 26.40± 0.06 3.00± 0.42 0.21± 0.15

MARD-Y3

25.83± 0.12 26.86± 0.14 2.60± 0.71 −25.82± 0.12 26.84± 0.14 − 2.62± 0.70

25.74± 0.11 26.70± 0.15 2.05± 0.66 0.31± 0.15

properties, e.g., the g-r at z∼0.4 and the r-i at z∼0.7— bothapproximately tracing the rest-frame U -B color— one findsonly a weak (≈-0.03 mag) signature for color evolution thatis very likely driven by the intrinsic uncertainties and scatterof the RS model itself. The notably higher scatter in g-r be-yond z ∼ 0.4 and in r-i beyond z ∼ 0.6, while reflecting bothhigher measurement uncertainties and that these bands aretracing rest frame portions of the SED that are most sen-sitive to recent star formation, could be an indication thata minority population of “bluer” hosts are actually enteringthe cross-matched sample.

In summary, our analysis does not suggest any ma-jor shift happening as a function of redshift in the stellarpopulation properties of the radio loud AGN host galaxiesout to z ∼ 0.8. This places limits on the suggested transi-tion in the cluster radio AGN from a Low Excitation Ra-dio Galaxy (LERG) dominated to a High Excitation Ra-dio Galaxy (HERG) dominated population (Bırzan et al.2017). A direct classification as HERG or LERG would re-quire spectra, which are currently not available for signifi-cant numbers of the AGN hosts we study here.

3.3 Luminosity function

We construct radio LFs by counting the excess of radio AGNtoward RM-Y3 and MARD-Y3 galaxy clusters to study theirevolution to z ∼ 1. In addition, we construct the LF from thecross–matched sample for the purpose of cross-comparisonwith the LF of the complete sample. In all cases we apply theredshift dependent k-correction with a spectral index of -0.7to estimate the luminosity at the same rest frame frequencyfor all redshifts.

In the following subsections we describe the LF con-struction in detail (Sections 3.3.1 and 3.3.2), present themodeling (Section 3.3.3) and best fit parameters (Sec-tion 3.3.4), compare the LF of the complete sample withthat of the cross–matched sample (Section 3.3.5) and thenfinally discuss how our results compare to those from previ-ous studies (Section 3.3.6).

3.3.1 Statistical LF construction

This adopted method to construct cluster galaxy LFs usingstatistical background subtraction is described in detail inprevious works (Lin et al. 2004; Lin & Mohr 2007, G17).Briefly, we adopt the cluster redshift to estimate the ra-dio source luminosities for individual sources that lie withinan angular distance θ200c of the cluster center. We combinethe point sources lying within θ200c of all clusters in loga-rithmic luminosity bins. This then produces a combinationof the luminosity function of the true cluster radio AGNtogether with the contamination from foreground or back-ground radio AGN that are randomly superposed on thecluster. We then build a model of the contamination usingthe logN − logS extracted for the full SUMSS population,cycling through the cluster list using the cluster redshift totransform from radio source flux density to luminosity andscaling by the associated solid angle of the virial region foreach cluster. For the reasons discussed in G17, we then sub-tract the contamination model and divide the resulting LFsby the sum of the virial masses of the clusters that contributeto each of the luminosity bins. In doing this we are normal-izing the LF in units of M−1

, which is a convenient proxyfor volume in the case of collapsed objects like clusters andgroups. In Section 3.4 we study the halo occupation numberor HON of radio AGN using the LF redshift evolution de-rived here and show that the number of radio galaxies scalesapproximately linearly with the cluster halo mass.

For the RM-Y3 catalog there are 3601 (1449, 2152) total(background, background subtracted) radio AGN observedabove the previously discussed flux limits. In the MARD-Y3case the corresponding numbers are 910 (455, 455). The to-tal number of AGN in the RM-Y3 cluster sample allow usto estimate the incompleteness in the cross–matched sam-ple, and this indicates that the ∼ 60 percent completenessestimated from the surface density profiles for our matchingcriteria is reasonably accurate (see Section 2.4).

We validate our LF construction code and our methodby analyzing simulated samples that are 10 times the sizeof our radio source catalogs and that are created using thebest fit LFs reported in Table 2 (for density evolution). Werecover the input parameters to within the statistical uncer-tainties.

3.3.2 Construction of LF for cross–matched sample

Although the cross–matched sample is estimated to be only≤ 60 percent complete and to have contamination of 15 per-cent, we nevertheless construct the LF to allow for com-parison to the statistically derived LF. For this purpose,we use the subset of SUMSS sources with identified opticalcounterparts whose redshifts and sky locations place themwithin a RM-Y3 cluster (as noted earlier, we do not do cross–matching for the radio AGN in the much smaller MARD-Y3cluster sample). In this case we adopt the cluster redshift forall SUMSS sources from that cluster, convert from flux toluminosity and build up a vector in logarithmic luminosityspace that contains the sum of all identified sources. We di-vide this vector by the sum of the virial masses of all theclusters that could have contributed to each luminosity bin(whether they actually contain a radio AGN or not), using

MNRAS 000, 000–000 (0000)


22 23 24 25 26 27 2810−20

10−19

10−18

10−17

10−16

10−15

10−14

10−13

dn/d

logP

[M−1

]

RM-Y3

Gupta+170.1<z<0.250.25<z<0.50.5<z<0.78

22 23 24 25 26 27 28

log[P/(W Hz−1)]

0

1

2

3

4

5

Rat

io

22 23 24 25 26 27 2810−20

10−19

10−18

10−17

10−16

10−15

10−14

10−13

dn/d

logP

[M−

1

]

MARD-Y3

Gupta+170.1<z<0.40.4<z<1.

22 23 24 25 26 27 28

log[P/(W Hz−1)]

0

1

2

3

4

5

Rat

ioFigure 6. SUMSS based 843 MHz cluster radio AGN LFs observed from RM-Y3 (left) and MARD-Y3 (right) catalogs. Upper panels

show the LFs obtained using the statistical background subtraction algorithm described in Section 3.3.1. The Poisson uncertainties arerepresented by error bars. The datasets are fitted with the LF model by varying y, x and γ (density and luminosity evolution) parameters

as discussed in Section 3.3.3. Different lines indicate the best fit model LFs (see Table 2). For convenience, the luminosity bins containing

negative values in the background subtracted counts are represented as points at the bottom of the figure. Pink points and line representthe best fit model and model uncertainties from G17. Lower panels show the ratio between the measurements and the best fit model

for the lowest redshift bin in this work. While fitting we divide the cluster samples into 15 redshift bins, but for this figure we show theresults in only two or three redshift bins to reduce the Poisson noise.

the minimum luminosity probed by the cluster given theSUMSS flux limit and the cluster redshift.

This method is attractive in that there is no need tosubtract off contamination from randomly superposed ra-dio AGN. This reduces the Poisson noise in the final LFand is helpful in better defining the behavior of the rare,most luminous radio AGN. However, given the incomplete-ness and contamination in the cross–matched sample, wedo not expect perfect agreement with the estimates of theLF extracted statistically using the method described in theprevious section. Comparisons are presented in Section 3.3.5below.

3.3.3 LF modeling

We fit our LFs using the functional form from Condon et al.(2002), given as

log

(dn

d logP

)= y−

[b2 +

(logP − x

w

)2]1/2−1.5 logP, (8)

where the parameters b, x and w, control the shape of theLF and y is its amplitude.

Assuming that the overall shape of the LFs remains con-stant, the only changes can be in the density and luminosityof the sources (Machalski & Godlowski 2000). The densityevolution corresponds to a vertical shift in the LFs and canbe quantified as

dn(z)

d logP=

dn(z = zC)

d logP×(

1 + z

1 + zC

)γD, (9)

similarly, the luminosity evolution corresponds to a horizon-tal shift in the LFs because of the evolving luminosities of

the sources

P (z) = P (z = zC)×(

1 + z

1 + zC

)γP, (10)

where zC = 0.47 corresponds to the median redshift of theRM-Y3 cluster sample and for comparison we take the samezC for the MARD-Y3 cluster sample. γD and γP correspondto the power law index for density and luminosity evolution,respectively, of the LFs.

We again perform an MCMC analysis with the Cashstatistic to fit the LFs. Following G17, we fit for the AGNpart of the LF, fix the values of the two shape parametersb and w to those determined in Condon et al. (2002) andvary x and y along with the density or luminosity evolutionpower law index. As reported in a previous study using X-ray selected clusters (G17), we find consistent results whenb and w are fixed to either Condon et al. (2002) or Best &Heckman (2012) best fit values. We evaluate the likelihoodof a given model by scaling the LF model with the totalcluster mass contributing to each luminosity bin and thenadding the statistically determined background number ofgalaxies to the corresponding luminosity bin.

We correct our LF amplitudes by scaling them with adeprojection factor (Dprj) that accounts for the cylindricalto spherical projection bias of radio AGN. This correctionis very small because the radio AGN in clusters have a highNFW concentration; we find Dprj ∼ 0.92.

3.3.4 Best fit LF parameters and uncertainties

LFs for the full sample constructed statistically (Sec-tion 3.3.1) are shown in the upper panels of Fig. 6 for RM-Y3 (left) and MARD-Y3 (right) catalogs. We choose all

MNRAS 000, 000–000 (0000)


26.2526.5026.7527.0027.25

x

0.0

1.5

3.0

γD

25.4

25.6

25.8

26.0

y

−0.250.

000.25

0.50

0.75

γP

26.25

26.50

26.75

27.00

27.25

x

0.0

1.5

3.0

γD

y

−0.3 0.

00.3

0.6

γP

RM-Y3MARD-Y3

Figure 7. Joint LF parameter posterior distributions for a com-

bined density (γD) and luminosity (γP) evolution fit to the ra-dio AGN LFs (RM-Y3 in blue; MARD-Y3 in green). Parameter

values are reported in Table 2. For this fit, we adopted priors

on the luminosity evolution parameter γP = 0.30 ± 0.15, deter-mined through a direct analysis of the radio luminosity to stellar

mass relation as described in Section 3.2.1. The smaller MARD-

Y3 sample prefers a fit with fewer extreme, high luminosity AGN.

sources to construct the LF with a flux limit at the 100 per-cent completeness of the SUMSS catalog as described in Sec-tion 2.1. In this figure, we plot the background subtractedobserved counts in larger luminosity bins and in three red-shift bins. However, this figure does not represent the fittingmethod, where the observed counts are divided into muchfiner luminosity bins and in 15 redshift bins (with similarnumbers of clusters in each bin) to get the model parame-ters. We also show the best fit model and model uncertaintiesfrom G17 in pink, where the median redshift of that sampleis z = 0.1.

The bottom panels of Fig. 6 show the ratios of themeasured LFs for both cluster samples and at different red-shift bins to the best fit model in the lowest redshift bin inthis work. It is visually apparent that the optically selectedRM-Y3 and X-ray selected MARD-Y3 samples provide sim-ilar radio AGN LFs over this redshift range. Because theMARD-Y3 cluster sample is smaller, we show only two red-shift ranges.

In the lower panels one can see some evidence of achange in LF shape with increasing redshift. For instance,there is a larger increase in the LF amplitude at lower lu-minosities but for luminosity log [P/(W Hz−1)] > 1026.5, noevolution with redshift is evident. We have not attemptedindependent fits within each redshift range where all param-eters are free to vary, simply because of the limited sizes ofour AGN samples. However, with future samples it should bepossible to further examine whether there is more evolutionat lower radio power than at higher.

Table 2 contains the best fit parameters for the LFs forthe scenarios where either pure density evolution or pure

luminosity evolution is taken into account. As expected, wefind that the measured LFs alone are insufficient to simul-taneously constrain density and luminosity evolution in theMCMC analysis.

The parameter uncertainties shown in Table 2 aremarginalized over uncertainties in the λ-mass relation whenRM-Y3 catalog is used and the LX-mass relation when theMARD-Y3 sample is used. As an example, we marginal-ize over the uncertainties in the λ-mass relation describedin Section 2.3.1 by first measuring the luminosity functionsunder single parameter excursions of ± 2-σ for the λ-massparameters Aλ, Bλ and γλ. We then extract the derivativesof the LF parameters y, x and γ with respect to each of theλ-mass parameters and finally propagate the uncertaintiesin the λ-mass relation to the luminosity function parametersusing Gaussian error propagation, further assuming no pa-rameter covariance in the λ-mass relation parameters. Thisis a good approximation as there are negligible degeneraciesbetween the parameters of the λ-mass relation (McClintocket al. 2019). We find that the contributions to the LF pa-rameter uncertainties from the remaining uncertainties inthe λ-mass relation are smaller than the statistical or sam-ple size contributions to the uncertainties. Nevertheless, wepresent overall combined constraints (including the system-atics from uncertainties in λ-mass) in Table 2.

We also use the constraints on the radio luminosity evo-lution with redshift at fixed stellar mass (Section 3.2.1), tosimultaneously constrain density and luminosity evolution.These results are shown in the third set of results for eachsample in Table 2. Adopting the best fit value and uncer-tainty in γPM = 0.30 ± 0.15 as a prior on the luminosityevolution, we estimate joint parameter constraints on lumi-nosity and density evolution parameters of the LF. Fig. 7shows the 2-D marginalized 1-σ MCMC constraints for lu-minosity function parameters and it reveals the significantparameter covariance between the shape and amplitude pa-rameters x and y, which is boosting the fully marginalizeduncertainties on each parameter.

There is a statistically significant shift in the joint spaceof shape and amplitude parameters between the RM-Y3 andMARD-Y3 samples. This shift is apparent as a ∼2σ offsetin the fully marginalized posterior of the shape parameterx in Table 2. We expect that this difference is driven by asteeper fall–off of the RM-Y3 sample at highest radio powers,which then drives corresponding changes in the amplitudedue to the correlation between the shape and amplitude pa-rameters. The MARD-Y3 sample is smaller, and the highestluminosity portion of the LF with log [P/(W Hz−1)] > 1027

is more poorly probed than in the RM-Y3 sample, and forthat reason we restrict the fit for the smaller sample to lowerpower AGN. Thus, the portion of the LF causing this ap-parent difference between the radio AGN LF of these twosamples is only probed in one of the two samples. With fu-ture, larger X-ray selected samples from eROSITA (Predehlet al. 2010; Merloni et al. 2012) it should be possible to probethese highest luminosity, rarest radio AGN more preciselyand better understand any possible differences between X-ray and optically selected cluster samples.

The best fit density evolution parameters for the X-ray and optically selected cluster samples are statisticallyconsistent, but the RM-Y3 sample suggests a more rapidevolution. In the combined density and luminosity evolution

MNRAS 000, 000–000 (0000)


23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0

10−17

10−16

10−15

dn/d

logP

[M−

1

]

0.1<z<0.250.25<z<0.50.5<z<0.78

23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0log[P/(W Hz−1)]

100

(dn/d

logP

) S/

(dn/d

logP

) D

Figure 8. The cluster radio AGN luminosity functions obtained

using the incomplete optically cross–matched AGN sample (Sec-

tion 3.3.2) for the RM-Y3 clusters is in the upper panel. Theratio (lower panel) between the statistical (subscript S) (see Sec-

tion 3.3.1 and Fig. 6) and cross–matched (subscript D) LFs is

shown for three redshift bins. There is consistency for the mostluminous radio AGN (log [P/(W Hz−1)] > 25.5) where the com-

pleteness of the cross–matched sample is highest, but for lowerluminosity AGN the incompleteness increases (see Section 3.3.5).

models, the density evolution parameter for the MARD-Y3is γD = 2.05 ± 0.66 and for the optically selected RM-Y3is γD = 3.00 ± 0.42. Again, these uncertainties include theunderlying uncertainties in the observable mass relations foreach cluster sample.

3.3.5 Comparison with the cross–matched sample

In Fig. 8, we present the 843 MHz LFs (top panel) in dif-ferent redshift bins, constructed using the sample of opti-cally cross–matched radio AGN as described in Section 3.3.2.We compare these LFs with those produced using statisticalbackground subtraction and for which the sample is com-plete, as described in Section 3.3.1 and shown in Fig. 6.

On the luminous end, the LFs are in good agreement,but at radio power log [P/(W Hz−1)] < 25.5, the LFs fromthe cross–matched sample are systematically lower in am-plitude than the statistically reconstructed LFs. Given theestimated completeness (∼ 60 percent) and contamination(∼ 15 percent) in the cross–matched sample (discussed inSection 2.4), some differences are expected. As described inSection 2.4, only the two most massive sub-classes of galaxies(log(M∗) > 10.9) are used in this cross matching so that thesample contamination can be kept at or below the 15 percentlevel.

The fact that the LF of the cross–matched sample un-derestimates the statistical LF mostly at the lowest radioluminosities in each bin may well be an indication of higher

contamination and incompleteness in the lowest flux radiobins, where sources have the largest positional uncertaintiesand are therefore more likely to be cross–matched to thewrong counterpart. Another effect that may be playing arole is that double tail radio sources may be resolved moreeffectively at lower redshift. Resolving such sources wouldcreate two radio sources and increase the chances that bothwould be cross–matched to the wrong counterpart.

The differences between the LFs calculated using thecross–matched and the complete sample pose challengesfor field LF studies with the SUMSS sample where cross-matching is required, but as described in Section 3.3.1 above,for the cluster radio AGN LF one need not use a cross–matched sample.

3.3.6 Comparison of LF redshift trends to previous results

Similar trends with redshift have been seen in previous stud-ies of field radio AGN LFs. LFs of optically selected Quasi-Stellar Objects (QSOs) at z ≤ 2.2 showed a luminosity evo-lution with γP = 3.2± 0.1 (Boyle et al. 1988). Machalski &Godlowski (2000) and Brown et al. (2001) studied a sampleof 1.4 GHz radio sources at low and intermediate redshiftsand suggested a luminosity evolution of γP = 3 ± 1 and4± 1, respectively. In a recent study, Pracy et al. (2016) de-rived 1.4 GHz LFs for radio AGN separated into LERGs andHERGs. They found that the LERG population displays lit-tle or no evolution, while the HERG population evolves morerapidly as γP = 7.41+0.79

−1.33 or γD = 2.93+0.46−0.47. HERGs have

bluer color and a weaker 4000 A break, which are indicationsof ongoing star formation activity. LERGs, however, appearto be preferentially located at the centers of groups or clus-ters and are fueled by feedback from their hot gas haloes (Lin& Mohr 2007; Kauffmann et al. 2008; Lin et al. 2010; Best& Heckman 2012). As presented in Section 3.2.2 above, oursample of cross–matched hosts of cluster radio AGN showno significant shifts in color out to z ∼ 0.8, and so presum-ably the population we are studying with our cluster radioAGN LF is a LERG population.

Smolcic et al. (2009) explored the cosmic evolution ofAGN with low radio powers (log [P/(W Hz−1)] < 25.7) outto z = 1.3 and found pure density evolution γD = 1.1± 0.1and pure luminosity evolution γP = 0.8 ± 0.1. Strazzulloet al. (2010) carried out a multi-wavelength analysis ofDeep Spitzer Wide-area InfraRed Extragalactic Legacy Sur-veys’ Very Large Array field (SWIRE VLA) and foundγP = 2.7± 0.3 and 3.7+0.3

−0.4 for AGN and starforming popu-lations, respectively. Similarly, McAlpine et al. (2013) stud-ied pure density and luminosity evolution for a combineddataset of ∼900 VLA observed galaxies in the field, find-ing γP = 1.18 ± 0.21 and 2.47 ± 0.12 for AGN and starforming galaxies, respectively. Janssen et al. (2012) demon-strated that in the local Universe a sub-population of LERGsare hosted in blue star forming galaxies, with these blueLERGs becoming increasingly important at higher radiopower. Thus, it is possible that the contribution of suchblue LERGs increases towards higher redshifts, renderingthe initial assumption that all AGN are hosted by red pas-sive galaxies invalid. Smolcic et al. (2017) studied a COS-MOS sample of radio AGN at 3 GHz out to z = 5 and con-

MNRAS 000, 000–000 (0000)


strained pure density evolution γD = 2.00 ± 0.18 and pureluminosity evolution γP = 2.88± 0.34.

Also for clusters, Green et al. (2016) have shown thatat least 14 percent of BCGs show a significant color offsetfrom passivity in a population of 980 X-ray detected clusters(0.03 < z < 0.5). In their table 2 and figure 16, they showthe offset to passivity as a function of X-ray luminosity ofhost clusters, and they find larger fractions of galaxies withoffset from passivity in high luminosity clusters, which intheir sample are preferentially at higher redshift. For sam-ples of X-ray and optically selected galaxy clusters, Sommeret al. (2011), show γP = 8.19 ± 2.66 and γD = 3.99 ± 1.24,respectively using 1.4 GHz detected radio AGN from theFIRST survey in a redshift range of 0.1 to 0.3. They alsofind a steep pure density evolution with γD = 9.40 ± 1.85for an X-ray selected sample of galaxy clusters. In a recentwork, Bırzan et al. (2017) investigated AGN feedback in alarge sample of SZE selected clusters from SPT and ACTsurveys and found ∼ 7 times more SUMSS sources in z > 0.6clusters than in the z < 0.6 sample, which they suggest maybe due to the differences in the feedback mechanisms ontothe super massive black holes (SMBHs) in the low and highluminosity sources. In another recent work, Lin et al. (2017)constructed the radio LFs for 1.4 GHz sources in clustersout to z ∼ 1 and found an over-abundance of radio AGNin clusters compared to the field population (see also Lin &Mohr 2007; Best et al. 2007). They find that cluster galaxiesat z > 0.77 are about 1.5 to 2 times more likely to be activein the radio compared to those in lower redshift clusters.In comparison to these previous studies, the current workis based on a large cluster sample that allows us to pushto higher redshifts and more importantly we present a firstanalysis to constrain both density and luminosity evolutionof LFs simultaneously.

3.4 Halo occupation number (HON)

We define the halo occupation number (HON) as the averagenumber of background subtracted radio AGN per clusterwith log [P/(W Hz−1)] > 25.5. We estimate the HON in astack of RM-Y3 and MARD-Y3 clusters in various mass binsto study the mass trends for observed cluster radio sources.We account for the redshift trends estimated for combineddensity and luminosity evolution in the previous section andsolve for the mass trends with the pivot redshift zC = 0.47.

Fig. 9 shows the HON of radio sources in RM-Y3 andMARD-Y3 clusters, where we also show the best fit powerlaw of the form

NRG = AH

(M200c

1.5× 1014

)BH(

1 + z

1 + zC

)γD, (11)

where NRG describes the average number of radio AGN ina cluster with log [P/(W Hz−1)] > 25.5 and AH and BH arethe normalization and mass trend of the power law bestconstrained to 0.019 ± 0.001 and 1.2 ± 0.1, respectively forRM-Y3 sample. For the MARD-Y3 sample, we find AH =0.021+0.013

−0.010 and BH = 0.68 ± 0.34, which is consistent withthe mass trend (at 1.5σ) for the RM-Y3 sample, but alsoonly ∼2σ away from BH = 0. The two datasets togethersuggest a trend BH ∼ 1. In fitting the relation, we adopt themean mass < M200c > of the clusters within each mass bin,and we have adopted the best fit density evolution presented

1014 1015

M200c [M]

10−2

10−1

NR

G/N

Clu

s

RM− Y3

MARD− Y3

Figure 9. HONs: The mean number of radio sources with

log [P/(W Hz−1)] > 25.5 per galaxy cluster as a function of clus-

ter mass at z = 0.47 using optically selected RM-Y3 (red) andX-ray selected MARD-Y3 (blue) clusters. The solid line is the

best fit power law model and the shaded region shows the 1-σ

model uncertainty. The extent of the shaded region shows therange of mass used in the analysis. The plot is presented at the

pivot redshift zC = 0.47 for both cluster samples, and the red-shift dependence is corrected using the measured redshift trend

(1+z)γD from the LF analysis, where γD is the density evolution

only result for each sample as presented in Table 2.

for the combined density and luminosity evolution model inTable 2 for each cluster sample.

In Fig. 9, we show the data points in finer mass bins forthe RM-Y3 sample and broader mass bins for the MARD-Y3 sample along with best fit model and 1-σ model uncer-tainties as the shaded region around the models. The HONfor the MARD-Y3 sample tends to lie below that of the RM-Y3 sample, but it is the number of radio AGN in the highestmass bin that most strongly suggests differences between thesamples. We have examined this and see that if we choosea higher luminosity cut log [P/(W Hz−1)] > 26.0 the uncer-tainties increase but the two samples also show more similarbehavior. The two mass trends are statistically consistent,suggesting a mass trend BH ∼ 1. This motivates our choiceof normalizing the LFs by the mass of the galaxy clusters.Such a scaling has been suggested before (Lin & Mohr 2007),but never with such a large sample of clusters where the sam-ple alone could demonstrate that the probability of a clustercontaining a radio AGN above a threshold luminosity scalesroughly linearly with the cluster halo mass. We discuss thisresult further within the context of our other measurementsin the following section.

We have further examined whether there is a trendin radio AGN luminosity as a function of cluster mass.In Fig. 10 we plot the radio AGN sample separated intothree different redshift ranges in the space of radio lumi-nosity versus cluster halo mass. The data provide no clearevidence for a cluster halo mass dependence of the ra-dio AGN luminosity. Thus, the approximately linear clus-ter halo mass dependence of the HON of radio AGN with

MNRAS 000, 000–000 (0000)


1014 1015

M200c [M]

24

25

26

27

28

log[P/(W

Hz−

1)]

0.1 ≤ z ≤ 0.25

0.25 ≤ z ≤ 0.5

0.5 ≤ z ≤ 0.8

Figure 10. The radio luminosities for the cross-matched clusterradio AGN sample are plotted versus cluster halo mass. Given

that the SUMSS catalog is flux limited, we separate the sam-ples into different redshift ranges (color coded). There is no clear

evidence for a cluster halo mass dependence on the radio AGN

luminosity.

log [P/(W Hz−1)] > 25.5 (see Fig. 9) cannot be explained byradio AGN being more luminous in higher mass clusters.

4 DISCUSSION

In this section we use the measurements of the cluster radioAGN properties and their evolution to z ∼ 0.8 presented inthe previous section to discuss environmental influences onradio AGN and also to examine the radio mode feedback asa function of mass and redshift within galaxy clusters.

4.1 Environmental influences on radio AGN

We discuss the key results of our study within the context ofpast studies and then turn to possible scenarios that couldexplain the trends in the cluster radio AGN we have pre-sented.

4.1.1 Cluster Radio AGN Properties in Context

The mass trend in the radio AGN HON presented in Sec-tion 3.4 (BH = 1.2± 0.1 for RM-Y3 and BH = 0.7± 0.3 forMARD-Y3) is similar to that reported for cluster galaxiesas a whole. In an analysis of the near-infrared (NIR) K-band properties of galaxies within 93 galaxy clusters andgroups using data from the Two Micron All Sky Survey(2MASS), Lin et al. (2004) reported a mass trend param-eter BH = 0.84 ± 0.04, indicating that in high mass galaxyclusters there are fewer galaxies per unit mass as comparedto low mass clusters. This trend is seen to remain largelyunchanged to z ∼ 1 in a sample of SPT SZE selected galaxyclusters (Hennig et al. 2017). The number of radio AGN perunit cluster mass, on the other hand, increases strongly withredshift for both of the samples studied here (γD = 3.0±0.4and 2.1± 0.7 for RM-Y3 and MARD-Y3, respectively).

The HON mass scaling and normalization taken to-gether with the centrally concentrated radial distributionpresented in Section 3.1, provides a picture of a cluster ra-dio AGN population within a cluster that is dominated bya single, radio luminous AGN lying in or near the clustercore. These galaxies are preferentially giant, passive ellipti-cals, and their probability of being radio loud increases withtheir stellar mass (Lin & Mohr 2007; Best et al. 2007). InFig. 9 we can see that, as a population, these galaxies ex-hibit a ∼10 percent probability of exceeding our adopted,nominal radio luminosity of log [P/(W Hz−1)] > 25.5 if theylie in a ∼ 6× 1014M cluster at z ∼ 0.5. The fact that theprobability of exceeding this threshold luminosity increaseswith cluster mass suggests a relationship between the condi-tions required for radio mode feedback and the cluster halomass.

One could argue that given the number of potentialgalaxy hosts for a radio loud AGN scales approximatelywith cluster mass (BH = 0.84 ± 0.04; Lin et al. 2004), itmay simply be that the probability of a radio AGN scalesapproximately with the number of potential hosts. However,given that the radio AGN lie preferentially in centrally lo-cated giant ellipticals (e.g., the BCG), this argument is notfully satisfying. There is only one BCG in each cluster, re-gardless of the cluster mass. Post-merger scenarios wherethere are multiple, similar mass BCG candidates that areon their way to merging through the action of dynamicalfriction occur both in low and high mass clusters and wouldtherefore not seem to explain the cluster halo mass trend weobserve.

It has been previously shown that the most massiveBCGs lie in the most massive galaxy clusters, although themass trend is very weak as MBCG ∼M0.26±0.04

200c (Lin & Mohr2004, note that these BCG stellar masses do not include theintracluster light), MBCG ∼ M0.24±0.08

200c (Zhang et al. 2016)and MBCG ∼M0.4±0.1

500c (Kravtsov et al. 2018). The halo masstrend in the HON is much steeper, suggesting that either (1)the galaxy mass dependence of a galaxy being radio loud isextremely steep, e.g., ∝ MB

BCG with B ∼ 4, which wouldbe inconsistent with the findings in Von Der Linden et al.(2007, figure 8) and Lin et al. (2017, figure 16), or (2) thatthe radio AGN HON mass trend is not driven by the massof the central galaxy alone.

The redshift trend in the HON and the density evolutionof the LF provides another interesting clue to environmentalinfluences on radio AGN. The host galaxy described abovein a 6× 1014M cluster at z ∼ 0.5 with a 10 percent chanceof hosting a radio AGN that exceeds our adopted radio lumi-nosity threshold would have a corresponding probability of∼25 percent at z ∼ 1 (equation 11). Because we know thatthe HON of the full galaxy population within the clustervirial region does not evolve with redshift (or evolves veryweakly) to z ∼ 1 (Hennig et al. 2017) and we know that BCGmass growth is rather slow over this redshift range (1.8 to1.2 times mass increase from z = 1 to the present; e.g,. Lid-man et al. 2012; Burke et al. 2015), it would be difficult toargue that the radio AGN population trends we are seeingare related to either galaxy number or galaxy host mass. Astrong possibility is that there is an environmentally driveneffect that is connected to the cluster halo mass and that ismore efficient at higher redshift.

Another important clue is that the typical radio lumi-

MNRAS 000, 000–000 (0000)


nosity at fixed host stellar mass increases only modestly withredshift as (1+z)0.30±0.15 (Section 3.2.1). This suggests thatthe radio mode events at high and low redshift are simi-lar (see also Galametz et al. 2009; Hlavacek-Larrondo et al.2012, and references therein), but that they are simply morefrequent within cluster halos at higher redshift. Moreover,our samples provides no evidence that radio AGN luminos-ity depends on the cluster halo mass.

4.1.2 Confining Pressure of the ICM

Of course, the cooling gas from the ICM could affect theradio activity. The radio-loud fraction increases for BCGsclosest to the peak in the ICM emission. This suggests thatthe availability of a fuel supply of cooling gas from thehalo environment impacts or enhances AGN activity in themost massive galaxies (e.g. Stott et al. 2012). The emissionlines from BCGs (principally Hα) indicate the presence of astrong cooling cluster core that has been shown to generallyhost more powerful radio sources. For BCGs in line emit-ting clusters, the X-ray cavity power correlates with boththe extended and core radio emission, suggestive of steadyfueling of the AGN in these clusters (Hogan et al. 2015).However, there is no clear mass or redshift dependence ofthe fraction of clusters with cool cores (Semler et al. 2012;McDonald et al. 2013), so it seems unlikely that central cool-ing of the ICM is responsible for the strong cluster halo massand redshift trends that we observe in the cluster radio AGNpopulation.

In a recent work, Lin et al. (2018) studied a sample of2300 radio AGN at z < 0.3 to investigate the likely sourcesof AGN activity in massive galaxies. They found that fortriggering the radio emission, both the stellar mass and thedark matter halo mass play an important role in both cen-tral and satellite galaxies. On the other hand, they foundno convincing evidence linking the elevated radio activity inmassive halos to the higher galaxy density therein. They alsofound that ICM entropy, cooling time and pressure are play-ing roles in triggering radio mode feedback. Their workinghypothesis is that stellar mass loss from evolved stars is thesource of the material accreted, and that the ICM pressureplays a role in confining that fuel within the host galaxy,making it more likely to be accreted.

This scenario is interesting within the context of ourresults, because the ICM pressure increases strongly withcluster mass and redshift. Moreover, central galaxies wouldbe preferred because the ram pressure stripping by the ICMof the stellar mass lost from evolved stars would be muchlower or even absent in central giant ellipticals that havesmall peculiar velocities. Recent ICM studies of cluster sam-ples spanning a similar redshift range to that of our radioAGN study have examined ICM mass fraction, ICM temper-ature, X-ray luminosity and an integrated ICM pressure YX

(e.g. Chiu et al. 2016, 2018; Bulbul et al. 2019, and ref-erences therein). In these studies the ICM mass fractionis observed to increase with cluster mass and, at a fixedmass, to remain roughly constant with redshift. The ICMdensity profiles outside the central core regions have beenshown to evolve approximately self-similarly with redshift(McDonald et al. 2013). ICM temperature increases withcluster mass and evolves with redshift roughly self-similarly,implying higher ICM temperatures at higher redshift for a

cluster of a given mass. Taken together, these results im-ply a confining pressure P around the central giant ellipti-cal that scales with mass as P ∝ M and with redshift asP ∝ [E(z)]8/3. Without a model that connects the confin-ing pressure to the radio mode feedback it is not possible tocomment on whether these similarly strong mass and red-shift dependences in central confining pressure and the prob-ability of a centrally located giant elliptical being radio loudare pure coincidence or indicative of a physical link.

4.1.3 Mergers of Infalling Gas Rich Galaxies with BCG

Another possible scenario that appears to be consistent withthe observations would be the interaction or merger of an in-falling galaxy that has residual star formation with a central,giant elliptical. Such an infalling galaxy would have to be onan approximately radial orbit, and so such events would beexpected to be rare. But the population of potential gas rich,infalling galaxies would scale roughly as the mass of the clus-ter and would also increase with redshift. Specifically, clus-ters with M200 > 3 × 1014M have blue fractions that areapproximately constant as a function of cluster mass, but theblue fractions increase with cluster redshift from 20 percentat z ∼ 0.1 to ∼50 percent at z ∼ 1 (Hennig et al. 2017).Thus, the number of potential merging, gas rich, infallinggalaxies increases with the cluster virial mass and also in-creases with redshift, providing a potential explanation forthe trends we report here in the cluster radio AGN.

Studies of BCG growth and the stellar mass–size rela-tion for quiescent galaxies over this same redshift range havesuggested that the dominant mode of growth for central gi-ant ellipticals is through merging with low mass galaxies(Burke et al. 2015). Another study of BCGs in 14 galaxyclusters between z = 0.84 and z = 1.46 indicates that 3of the 14 BCGs are likely to experience a major mergerwithin 600 Myr, suggesting that mergers with giant ellipti-cals are the primary mode for BCG growth; however, theresults from this small sample do not exclude the possibilitythat minor mergers could play an important role in shap-ing how central giant ellipticals appear today (Lidman et al.2013). In the process of merging, the gas rich infalling galaxywould deliver its gas to the BCG. Central cluster galaxies areknown to have reservoirs of molecular gas that are detectedthrough their CO line emission at low redshifts (e.g. Edge2001; McNamara et al. 2014; Temi et al. 2018; Vantyghemet al. 2019; Rose et al. 2019) and at redshifts as high asz = 1.7 (Webb et al. 2017). These molecular gas clouds areobserved to have line of sight velocities of the order of ∼ 200to 300 km s−1, which would support a chaotic cold accretiontype model in BCGs (e.g., David et al. 2014; Tremblay et al.2016). However, stronger evidence that mergers of infalling,gas rich galaxies with central giant ellipticals are responsi-ble for feeding and triggering the AGN accretion that leadseventually to radio mode feedback is needed to build con-fidence that this is a driver of the cluster AGN mass andredshift trends observed in the current work.

We note here also that ram pressure stripping will re-move gas from any infalling, gas rich galaxies, and this lowentropy gas will naturally sink toward the cluster center.The supply of this low entropy, sinking gas would increasewith cluster mass because there are more infalling, gas richgalaxies in higher mass clusters. Moreover, it would increase

MNRAS 000, 000–000 (0000)


with redshift, because cluster galaxy populations within thevirial region R200c have higher blue fractions– and thereforehigher gas content– at higher redshift (e.g., Hennig et al.2017). As with the previous scenario of merging, this sce-nario deserves further study.

4.2 Radio AGN feedback

To make an estimate of the radio mode feedback from AGNin clusters, we first calculate the mean total cluster radioAGN power PRadio using our measured LF extracted fromthe analysis of the RM-Y3 cluster sample (the case witha combination of luminosity and number density evolutionpresented in Table 2). We multiply the LF at a given red-shift with the mass of the cluster of interest and integrate theproduct of the radio power and the LF in the radio powerrange of 1023 to 1028 WHz−1 to get the expected averageradio power at the rest frame frequency of 843 MHz. Thisrange of power is selected, because it is comparable to theminimum and maximum radio powers of the radio AGN ob-served in our sample of clusters. Moreover, this radio powerlower limit is close to that marking the transition from astar forming dominated to an AGN dominated radio LF.

In Fig. 11, we show the mean total radio power (in col-orbar) as a function of cluster mass and redshift. There areroughly two orders of magnitude in dynamic range of themean radio power over the mass and redshift range exploredhere. The mean radio power is approximately 10× higher for1015M clusters than for 1014M, consistent with what wewould expect given the mass dependence of the halo oc-cupation number (Section 3.4). Moreover, there is a strongredshift dependence that leads to a similar ∼10× increasein mean radio power for a cluster of a given mass at z = 1in comparison to z = 0. This behavior follows from the mea-sured redshift trends in the density evolution of the radioLF (Table 2).

Studies of ICM cavities in ensembles of clusters contain-ing radio galaxies (Cavagnolo et al. 2010; Hlavacek-Larrondoet al. 2012, 2015) have demonstrated correlations betweenthe radio power and the amount of work done to createthe cavities in the ICM. Thus, to estimate the typical ra-dio mode feedback in clusters as a function of redshift, weuse the mean total radio power calculated above togetherwith the correlation between radio power and cavity powerfrom Cavagnolo et al. (2010). Specifically, we take our esti-mated 843 MHz radio power and convert it to an expected1.4 GHz radio power using the spectral index α = −0.7 at allredshifts. Further, we change units from W to erg s−1 andestimate the total radio luminosity L1400 by scaling the es-timated radio power by 1.4 GHz. We then use the Cavagnoloet al. (2010) relation to estimate the cavity power Pcav

Pcav = 5× 1043

(L1400

1040 erg s−1

)0.7

erg s−1. (12)

This cavity power represents an estimate of the minimummechanical feedback into the ICM. We calculate this esti-mate of the radio mode feedback as a function of mass andredshift as for the mean total radio power Pradio before.

The bulk of this radio mode feedback is concentrated inthe cluster core ( 2

3of the cluster radio AGN in our sample

lie within 0.1R200, corresponding to the central 0.1 percentof the cluster virial volume). To place this feedback energy

in context, we compare it to the X-ray radiative losses fromthe core region. Specifically, we measure the core X-ray lumi-nosities within 0.1R500 using and ensemble of SZE selectedgalaxy clusters that have been observed with the XMM-Newton X-ray observatory. This sample of 59 clusters with0.2 < z < 1.5 has been studied extensively in Bulbul et al.(2019), where both core included and core excluded quanti-ties have been presented.

We use the measurements of the core luminosities fromthat analysis together with mass and redshift measurementsfor the subset of the galaxy cluster sample where the core re-gion of interest is larger than the XMM-Newton point spreadfunction (PSF). The best fit core (≤ 0.1R500) X-ray lumi-nosity to mass relation that we find is

PXray = 16.88+1.53−1.40 × 1044erg s−1

(M500

Mpiv

)2.4±0.2

(E(z)

E(zpiv)

)7/3((1 + z)

(1 + zpiv)

)−0.7±0.4

, (13)

where Mpiv and zpiv are 6.35 × 1014 M and 0.45, respec-tively. In addition, we find a log normal intrinsic scatter of0.60+0.06

−0.05 in this relation, which is considerably larger thanthe scatter of the total cluster X-ray luminosity to mass re-lations presented for the same sample (∼ 0.3). This is notsurprising, because it has been long established that varia-tions in the structure of cluster cores are the primary driverof the scatter in the X-ray luminosity at fixed temperature(Fabian 1994; Mohr & Evrard 1997) or mass.

We note here that this X-ray core luminosity to massscaling relation is constrained using clusters in the massrange above 3 × 1014M and over the bulk of the redshiftrange of interest. In the following analysis we extrapolatethis relation to 1014M to make estimates over the full massrange where we study the cluster radio AGN LF. Moreover,we emphasize that this is the average central X-ray luminos-ity within a region that is a fraction of the virial region. Itis not the luminosity within a cooling radius where the ICMis estimated to be radiatively unstable. Our goal here is toexamine typical radio mode feedback in the cluster core tothe typical X-ray radiative losses in the core.

In the right panel of Fig. 11, we show the ratio betweenthe estimated mean radio mode feedback and the mean X-ray radiative losses. We find that the ratio between the radiocavity power and the core X-ray luminosity is correlatedwith the redshift of the clusters and is anti-correlated withits mass. For instance, the ratio of the radio feedback to X-ray radiative losses for a 1014M galaxy cluster is ∼ 2 timeslarger at z ∼ 1.05 as compared to the ratio at z ∼ 0.05. Onthe other hand the ratio is ∼ 50 times larger for a 1014Mgalaxy cluster as compare to a cluster with mass 1015M.

While these mass and redshift trends are interesting, theabsolute value of the ratio suffers from several uncertainties.For example, it could be shifted up or down simply by chang-ing the radius within which we estimate the X-ray radiativelosses. Moreover, we have used the Pcav estimated from theentire radio AGN population, whereas only ∼ 60 percent ofthat population lies at ≤ 0.1R500. Finally, our estimate ofthe mechanical feedback Pcav is derived using the energy re-quired to evacuate the cavities in the ICM observed arounda sizeable number of clusters. Pcav serves as a kind of lowerlimit to the actual mechanical feedback, with some authors

MNRAS 000, 000–000 (0000)

Cluster Radio AGN to z∼1 170.

050.

150.

250.

350.

450.

550.

650.

750.

850.

951.

05

z

14.014.114.214.314.414.514.614.714.814.915.0

logM

500

[M

]

24.50

24.75

25.00

25.25

25.50

25.75

26.00

26.25

log(Pra

dio )

[WH

z −1]

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0.85

0.95

1.05

z

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

14.9

15.0

logM

500

[M

]

0.15

0.30

0.50

1.00

2.50

5.00

8.50

12.00

Pcav /

PX

ray

Figure 11. Mean radio power at 843 MHz (left) of cluster radio AGN as a function of cluster mass and redshift calculated using the

radio LF presented in Section 3.3. On the right, we plot the ratio of the estimated mechanical feedback energy Pcav from the radioAGN to the central X-ray luminosities (r < 0.1R500) from the ICM as a function of cluster mass and redshift (see Section 4.2) using the

relationship between feedback energy and radio power presented in Cavagnolo et al. (2010). We note that the X-ray core luminosities are

well constrained at M500 > 3× 1014M (Bulbul et al. 2019).

arguing the total feedback could be a factor of 4 to 16 timeshigher (e.g., Cavagnolo et al. 2010).

Our current estimates indicate that the average radiomode feedback within clusters is comparable to or smallerthan the average central radiative losses within 0.1R500 forclusters with M500 & 5 × 1014 M at redshifts up to z ∼1 that we probe here. It is within this core region whereone can identify cool core structures within the ICM andwhere it is posited that the feedback from radio AGN may beplaying a crucial role in replacing the radiative losses from X-ray emission and preventing a cooling instability or coolingflow (e.g. Fabian 2012). Thus, in this mass range one mightexpect it to be more likely for cool core structures to emergeand for there to be no strong redshift trends. Indeed, in SZEselected cluster samples where the selection is unaffectedby the presence or absence of cool core structures, it hasbeen demonstrated that there is no significant evolution inthe cool core fraction with redshift for clusters with massesM500 > 3 × 1014M (Semler et al. 2012; McDonald et al.2012).

At lower masses the mean mechanical feedback fromradio mode feedback is many times larger than the core ra-diative cooling, and one might expect it to be less likelyfor cool core structures to emerge. We note that cool coresystems in groups and low mass clusters have been iden-tified in the nearby universe (Panagoulia et al. 2014), butit is not yet clear whether this represents a lower fractionof systems than is observed at higher masses. Moreover, inthis low mass range one might expect the excess of feed-back energy to increase the entropy within the cluster coreand beyond, perhaps even redistributing the ICM mass andleading to a reduction in the ICM mass fraction within thevirial region R500. In other words, the mass trend in the ra-tio of radio mode feedback and X-ray radiative losses impliesa mass dependent ICM mass fraction for clusters over the

mass range investigated here. Moreover, this is true over theentire redshift range studied here. In the local universe thistrend for lower mass clusters to exhibit lower ICM fractionswas first reported for a large cluster ensemble by Mohr et al.(1999) (using emission weighted mean X-ray temperaturesas a mass proxy). More recently, this mass trend has beendemonstrated in a study from group to cluster mass scalesusing the HIFLUGCS sample (see figure 2; Main et al. 2017)and in the SPT selected cluster sample, where there is noclear redshift trend over the full redshift range studied hereusing clusters with masses M500 > 3× 1014M (Chiu et al.2016, 2018; Bulbul et al. 2019). Thus, the measured massand redshift trends in the ICM mass fraction are qualita-tively consistent with the expectations, given the measuredmass and redshift trends of the ratio of radio mode feedbackand X-ray radiative losses.

Thus, the radio LFs for clusters with M200c > 1014Mand extending to redshift z ∼ 1 that we present here im-ply significant mean radio mode mechanical feedback thatoffsets or dominates the mean core X-ray radiative lossesfor all but the most massive clusters studied here (M500 ≥5 × 1014M). If the estimated radio mode feedback Pcav

underestimates the true radio feedback by a factor of 4 to16, then at no mass scale would the typical, observed radia-tive losses within 0.1R500 be important. We emphasize thatthere is significant scatter σln PXray = 0.6 in the X-ray ra-diative losses at fixed mass and redshift, and that the radiogalaxy population is rare and therefore there is significantstochasticity in the radio mode feedback as well. We use themeasured LFs and trends with mass and redshift to examinethe stochasticity, finding that the standard deviation in thelog of the mean radio luminosity varies from σln PRadio = 0.3for the 1015M clusters at z ∼ 1 (where radio AGN aremost abundant) to σln PRadio = 0.6 for 1014M groups atz ∼ 0 (where radio AGN are least abundant). These vari-

MNRAS 000, 000–000 (0000)


ations in both feedback and radiative losses would lead tothe emergence of systems where cooling would dominate overfeedback and the cool cores we observe could form. Once thecool core starts to form there is evidence of enhanced radiomode feedback, suggesting that the cooling ICM could itselfdrive new radio mode feedback (Fabian 2012, see figure 5).

5 CONCLUSIONS

We report measurements of the properties of cluster radioAGN to z ∼ 1 employing the largest cluster ensembles ex-tending to high redshift ever used. These properties of ra-dio AGN include their radial distribution within the cluster,radio luminosity evolution at fixed stellar mass, luminosityfunctions (LFs) and halo occupation number (HON) abovea luminosity threshold. These measurements are made usingSUMSS selected sources observed at 843 MHz within opti-cally selected RM-Y3 and X-ray selected MARD-Y3 clustercatalogs that have been produced using the first three yearsof DES observations and the RASS X-ray survey.

We focus on the excess population of radio sources asso-ciated with the virial regions of these clusters. The medianredshifts of RM-Y3 and MARD-Y3 clusters are 0.47 and0.28, respectively, and the catalogs extend to z = 0.8 andbeyond. The mass of RM-Y3 (Rykoff et al., in prep) andMARD-Y3 (Klein et al. 2019) clusters is estimated usingthe richness-mass relation from McClintock et al. (2019) andthe LX–mass relation from Bulbul et al. (2019), respectively,where the mass ranges correspond to M200c > 1 × 1014Mand M200c > 3× 1014M, respectively.

We find that the radial profile of the sources in RM-Y3and MARD-Y3 catalogs is highly concentrated at the centerof the cluster over the whole redshift range and is consistentwith an NFW model with concentration c ∼ 140. With thisconcentration, approximately 2

3of the cluster radio AGN lie

within 0.1R200 of the cluster centers, which are defined usingthe cluster galaxies.

A study of the cross–matched hosts of the clusterradio AGN indicates that the AGN radio luminosity atfixed stellar mass is constant or increases only modestly as(1+z)0.30±0.15 with redshift. The broad band colors of thesehosts are consistent with the cluster red sequence color andremain so without any major changes over the full redshiftrange (see Section 3.2). We use the luminosity evolution con-straint to break the degeneracy in density and luminosityevolution for the cluster radio AGN LF.

We construct the LFs assuming that the overdensity ofradio AGN toward a cluster is at the redshift of the cluster,and we correct for the non-cluster sources by employing astatistical background correction (see Section 3.3). We findthat at fixed cluster halo mass, the cluster radio galaxies aremore numerous at higher redshift. We find best fit redshifttrends (1+z)γ in combined density and luminosity evolutionof γD = 3.00 ± 0.42 and γP = 0.21 ± 0.15, respectively forthe RM-Y3 sample. Evolution is statistically consistent butmore gradual for the X-ray selected MARD-Y3 sample: γD =2.05 ± 0.66 and γP = 0.31 ± 0.15. The uncertainties on theluminosity function parameters are marginalized over theuncertainties in the cluster observable-mass relations. Ourresults provide a clear indication that density evolution with

redshift dominates over luminosity evolution with redshift incluster radio AGN populations.

Furthermore, we estimate the halo occupation numberfor radio AGN above a fixed luminosity threshold in a stackof RM-Y3 and MARD-Y3 clusters using the LF evolutionidentified above. We show that the number of radio AGNabove a luminosity threshold scales with the cluster massas N ∝ MBH with BH = 1.2 ± 0.1 for the RM-Y3 sampleand with BH = 0.68 ± 0.34 for the MARD-Y3 sample, in-dicating a relationship between the probability of a clustercontaining a radio loud AGN and the cluster halo mass. Fur-thermore, we show that there is no compelling evidence fora dependence of radio AGN luminosity on cluster halo mass(see Section 3.4).

We use these measurements to inform a discussion ofthe environmental influences on radio mode feedback (seeSection 4.1). We consider two scenarios, one where the con-fining pressure of the ICM around the central giant ellipticalsis responsible for the observed radio feedback mode and an-other where the merger of infalling, gas rich galaxies withcentrally located giant ellipticals could also lead to the massand redshift trends we measure in the radio AGN popula-tion. We note also that even in the absence of merging, gasrich galaxies will lose their gas through ram pressure strip-ping, and this low entropy gas will sink to the cluster center,potentially providing fuel for radio mode accretion.

We go on in Section 4.2 to use the radio AGN LF to esti-mate the radio mode feedback as a function of mass and red-shift out to z ∼ 1 and compare that to the mean core X-rayradiative losses from the ICM at each mass and redshift. Theradio mode feedback dominates the core radiative losses inlow mass systems and is comparable to or smaller than thoseradiative losses for systems with M500 > 5 × 1014M overthe full redshift range. We note the imbalance of radio modefeedback and X-ray radiative losses is qualitatively consis-tent with what one would expect to explain the absence ofredshift evolution of the cool core population and the trendof increasing ICM mass fraction with mass observed withinclusters over the same mass and redshift range.

ACKNOWLEDGEMENTS

We thank Jeremy Sanders for helpful discussions. The Mel-bourne group acknowledges support from the Australian Re-search Council’s Discovery Projects scheme (DP150103208).The Munich group acknowledges the support of the In-ternational Max Planck Research School on Astrophysicsof the Ludwig-Maximilians-Universitat, the Max-Planck-Gesellschaft Faculty Fellowship program at the Max PlanckInstitute for Extraterrestrial Physics, the DFG Cluster ofExcellence “Origin and Structure of the Universe”, theVerbundforschung ’D-MeerKAT’ award 05A2017 and theLudwig-Maximilians-Universitat. AS is supported by theERC-StG ’ClustersXCosmo’ grant agreement 71676, and bythe FARE-MIUR grant ’ClustersXEuclid’ R165SBKTMA.

SPT is supported by the National Science Foundationthrough grant PLR-1248097. Partial support is also providedby the NSF Physics Frontier Center grant PHY-1125897 tothe Kavli Institute of Cosmological Physics at the Universityof Chicago, the Kavli Foundation and the Gordon and BettyMoore Foundation grant GBMF 947. This research used re-

MNRAS 000, 000–000 (0000)


sources of the National Energy Research Scientific Comput-ing Center (NERSC), a DOE Office of Science User Facilitysupported by the Office of Science of the U.S. Departmentof Energy under Contract No. DE-AC02-05CH11231.

Funding for the DES Projects has been provided bythe U.S. Department of Energy, the U.S. National Sci-ence Foundation, the Ministry of Science and Education ofSpain, the Science and Technology Facilities Council of theUnited Kingdom, the Higher Education Funding Council forEngland, the National Center for Supercomputing Applica-tions at the University of Illinois at Urbana-Champaign, theKavli Institute of Cosmological Physics at the Universityof Chicago, the Center for Cosmology and Astro-ParticlePhysics at the Ohio State University, the Mitchell Institutefor Fundamental Physics and Astronomy at Texas A&MUniversity, Financiadora de Estudos e Projetos, FundacaoCarlos Chagas Filho de Amparo a Pesquisa do Estado do Riode Janeiro, Conselho Nacional de Desenvolvimento Cientı-fico e Tecnologico and the Ministerio da Ciencia, Tecnologiae Inovacao, the Deutsche Forschungsgemeinschaft and theCollaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne NationalLaboratory, the University of California at Santa Cruz,the University of Cambridge, Centro de InvestigacionesEnergeticas, Medioambientales y Tecnologicas-Madrid, theUniversity of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Ei-dgenossische Technische Hochschule (ETH) Zurich, FermiNational Accelerator Laboratory, the University of Illi-nois at Urbana-Champaign, the Institut de Ciencies del’Espai (IEEC/CSIC), the Institut de Fısica d’Altes Ener-gies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universitat Munchen and the associated Ex-cellence Cluster Universe, the University of Michigan, theNational Optical Astronomy Observatory, the University ofNottingham, The Ohio State University, the University ofPennsylvania, the University of Portsmouth, SLAC NationalAccelerator Laboratory, Stanford University, the Universityof Sussex, Texas A&M University, and the OzDES Member-ship Consortium.

Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Obser-vatory, which is operated by the Association of Universi-ties for Research in Astronomy (AURA) under a cooperativeagreement with the National Science Foundation.

The DES data management system is supported bythe National Science Foundation under Grant NumbersAST-1138766 and AST-1536171. The DES participants fromSpanish institutions are partially supported by MINECOunder grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the Euro-pean Union. IFAE is partially funded by the CERCA pro-gram of the Generalitat de Catalunya. Research leading tothese results has received funding from the European Re-search Council under the European Union’s Seventh Frame-work Program (FP7/2007-2013) including ERC grant agree-ments 240672, 291329, and 306478. We acknowledge supportfrom the Brazilian Instituto Nacional de Ciencia e Tecnolo-gia (INCT) e-Universe (CNPq grant 465376/2014-2).

This manuscript has been authored by Fermi ResearchAlliance, LLC under Contract No. DE-AC02-07CH11359

with the U.S. Department of Energy, Office of Science, Of-fice of High Energy Physics. The United States Govern-ment retains and the publisher, by accepting the article forpublication, acknowledges that the United States Govern-ment retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form ofthis manuscript, or allow others to do so, for United StatesGovernment purposes. This manuscript has been authoredby Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Of-fice of Science, Office of High Energy Physics. The UnitedStates Government retains and the publisher, by acceptingthe article for publication, acknowledges that the UnitedStates Government retains a non-exclusive, paid-up, irrevo-cable, world-wide license to publish or reproduce the pub-lished form of this manuscript, or allow others to do so, forUnited States Government purposes.

REFERENCES

Abbott T. M. C., et al., 2018, ApJS, 239, 18

Aihara H., et al., 2011, ApJS, 193, 29

Annis J., et al., 2014, ApJ, 794, 120

Bartelmann M., 1996, A&A, 313, 697

Bertin E., Arnouts S., 1996, A&AS, 117, 393

Best P. N., Heckman T. M., 2012, MNRAS, 421, 1569

Best P. N., von der Linden A., Kauffmann G., Heckman T. M.,Kaiser C. R., 2007, MNRAS, 379, 894

Bharadwaj V., Reiprich T. H., Schellenberger G., Eckmiller H. J.,

Mittal R., Israel H., 2014, A&A, 572, A46

Bırzan L., Rafferty D. A., Nulsen P. E. J., McNamara B. R.,

Rottgering H. J. A., Wise M. W., Mittal R., 2012, MNRAS,

427, 3468

Bırzan L., Rafferty D. A., Bruggen M., Intema H. T., 2017, MN-RAS, 471, 1766

Blanton E. L., Clarke T. E., Sarazin C. L., Randall S. W., Mc-Namara B. R., 2010, Proceedings of the National Academy of

Science, 107, 7174

Bock D. C.-J., Large M. I., Sadler E. M., 1999, AJ, 117, 1578

Bocquet S., et al., 2019, ApJ, 878, 55

Boller T., Freyberg M. J., Trumper J., Haberl F., Voges W., Nan-dra K., 2016, A&A, 588, A103

Boyle B. J., Shanks T., Peterson B. A., 1988, MNRAS, 235, 935

Brown M. J. I., Webster R. L., Boyle B. J., 2001, AJ, 121, 2381

Bruzual G., Charlot S., 2003, MNRAS, 344, 1000

Bulbul E., et al., 2019, ApJ, 871, 50

Burke C., Hilton M., Collins C., 2015, MNRAS, 449, 2353

Calzetti D., Armus L., Bohlin R. C., Kinney A. L., Koornneef J.,

Storchi-Bergmann T., 2000, ApJ, 533, 682

Capasso R., et al., 2019a, MNRAS, 482, 1043

Capasso R., et al., 2019b, MNRAS, 486, 1594

Cash W., 1979, ApJ, 228, 939

Cavagnolo K. W., McNamara B. R., Nulsen P. E. J., Carilli C. L.,

Jones C., Bırzan L., 2010, ApJ, 720, 1066

Chiu I., et al., 2016, MNRAS, 455, 258

Chiu I., et al., 2018, MNRAS, 478, 3072

Condon J. J., Cotton W. D., Broderick J. J., 2002, AJ, 124, 675

David L. P., et al., 2014, ApJ, 792, 94

Desai S., et al., 2012, ApJ, 757, 83

Diemer B., Kravtsov A. V., 2015, ApJ, 799, 108

Dietrich J. P., et al., 2019, MNRAS, 483, 2871

Edge A. C., 2001, MNRAS, 328, 762

Ehlert S., et al., 2011, MNRAS, 411, 1641

Fabian A. C., 1994, ARA&A, 32, 277

Fabian A. C., 2012, ARA&A, 50, 455

MNRAS 000, 000–000 (0000)

http://dx.doi.org/10.3847/1538-4365/aae9f0

http://adsabs.harvard.edu/abs/2018ApJS..239...18A

http://dx.doi.org/10.1088/0067-0049/193/2/29

http://adsabs.harvard.edu/abs/2011ApJS..193...29A

http://dx.doi.org/10.1088/0004-637X/794/2/120

http://adsabs.harvard.edu/abs/2014ApJ...794..120A

http://adsabs.harvard.edu/abs/1996A%26A...313..697B

http://adsabs.harvard.edu/abs/1996A%26AS..117..393B

http://dx.doi.org/10.1111/j.1365-2966.2012.20414.x

http://adsabs.harvard.edu/abs/2012MNRAS.421.1569B

http://dx.doi.org/10.1111/j.1365-2966.2007.11937.x

http://adsabs.harvard.edu/abs/2007MNRAS.379..894B

http://dx.doi.org/10.1051/0004-6361/201322684

https://ui.adsabs.harvard.edu/#abs/2014A&A...572A..46B

http://dx.doi.org/10.1111/j.1365-2966.2012.22083.x


http://dx.doi.org/10.1093/mnras/stx1505



http://dx.doi.org/10.1073/pnas.0913904107

http://dx.doi.org/10.1073/pnas.0913904107

https://ui.adsabs.harvard.edu/#abs/2010PNAS..107.7174B

http://dx.doi.org/10.1086/300786

http://adsabs.harvard.edu/abs/1999AJ....117.1578B

http://dx.doi.org/10.3847/1538-4357/ab1f10

https://ui.adsabs.harvard.edu/abs/2019ApJ...878...55B

http://dx.doi.org/10.1051/0004-6361/201525648

http://adsabs.harvard.edu/abs/2016A%26A...588A.103B

http://dx.doi.org/10.1093/mnras/235.3.935

http://adsabs.harvard.edu/abs/1988MNRAS.235..935B

http://dx.doi.org/10.1086/320410

http://adsabs.harvard.edu/abs/2001AJ....121.2381B

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2003MNRAS.344.1000B&db_key=AST

http://dx.doi.org/10.3847/1538-4357/aaf230

http://adsabs.harvard.edu/abs/2019ApJ...871...50B

http://dx.doi.org/10.1093/mnras/stv450


http://dx.doi.org/10.1086/308692

http://adsabs.harvard.edu/abs/2000ApJ...533..682C

http://dx.doi.org/10.1093/mnras/sty2645

http://adsabs.harvard.edu/abs/2019MNRAS.482.1043C

http://dx.doi.org/10.1093/mnras/stz931

https://ui.adsabs.harvard.edu/abs/2019MNRAS.486.1594C

http://dx.doi.org/10.1086/156922

http://adsabs.harvard.edu/abs/1979ApJ...228..939C

http://dx.doi.org/10.1088/0004-637X/720/2/1066

http://adsabs.harvard.edu/abs/2010ApJ...720.1066C


http://adsabs.harvard.edu/abs/2016MNRAS.455..258C


http://adsabs.harvard.edu/abs/2018MNRAS.478.3072C

http://dx.doi.org/10.1086/341650

http://adsabs.harvard.edu/abs/2002AJ....124..675C

http://dx.doi.org/10.1088/0004-637X/792/2/94

http://adsabs.harvard.edu/abs/2014ApJ...792...94D

http://dx.doi.org/10.1088/0004-637X/757/1/83


http://dx.doi.org/10.1088/0004-637X/799/1/108

http://adsabs.harvard.edu/abs/2015ApJ...799..108D


http://adsabs.harvard.edu/abs/2019MNRAS.483.2871D

http://dx.doi.org/10.1046/j.1365-8711.2001.04802.x

http://adsabs.harvard.edu/abs/2001MNRAS.328..762E

http://dx.doi.org/10.1111/j.1365-2966.2010.17801.x

https://ui.adsabs.harvard.edu/#abs/2011MNRAS.411.1641E

http://dx.doi.org/10.1146/annurev.aa.32.090194.001425

http://adsabs.harvard.edu/abs/1994ARA%26A..32..277F

http://dx.doi.org/10.1146/annurev-astro-081811-125521

http://adsabs.harvard.edu/abs/2012ARA%26A..50..455F


Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013,

PASP, 125, 306

Galametz A., et al., 2009, ApJ, 694, 1309

Gitti M., Brighenti F., McNamara B. R., 2012, Advances in As-

tronomy, 2012, 950641

Green T. S., et al., 2016, MNRAS, 461, 560

Gupta N., et al., 2017, MNRAS, 467, 3737

Hennig C., et al., 2017, MNRAS, 467, 4015

Hlavacek-Larrondo J., Fabian A. C., Edge A. C., Ebeling H.,Sanders J. S., Hogan M. T., Taylor G. B., 2012, MNRAS,

421, 1360

Hlavacek-Larrondo J., Fabian A. C., Edge A. C., Ebeling H., AllenS. W., Sanders J. S., Taylor G. B., 2013, MNRAS, 431, 1638

Hlavacek-Larrondo J., et al., 2015, ApJ, 805, 35

Hogan M. T., et al., 2015, MNRAS, 453, 1201

Janssen R. M. J., Rottgering H. J. A., Best P. N., Brinchmann

J., 2012, A&A, 541, A62

Kauffmann G., Heckman T. M., Best P. N., 2008, MNRAS, 384,

953

Klein M., et al., 2018, MNRAS, 474, 3324

Klein M., et al., 2019, MNRAS, p. 1397

Kravtsov A. V., Vikhlinin A. A., Meshcheryakov A. V., 2018,Astronomy Letters, 44, 8

Kriek M., van Dokkum P. G., Labbe I., Franx M., Illingworth

G. D., Marchesini D., Quadri R. F., 2009, ApJ, 700, 221

Lidman C., et al., 2012, MNRAS, 427, 550

Lidman C., et al., 2013, MNRAS, 433, 825

Lin Y.-T., Mohr J. J., 2004, ApJ, 617, 879

Lin Y.-T., Mohr J. J., 2007, ApJS, 170, 71

Lin Y., Mohr J. J., Stanford S. A., 2004, ApJ, 610, 745

Lin Y., Partridge B., Pober J. C., Bouchefry K. E., Burke S.,

Klein J. N., Coish J. W., Huffenberger K. M., 2009, ApJ, 694,992

Lin Y.-T., Shen Y., Strauss M. A., Richards G. T., Lunnan R.,

2010, ApJ, 723, 1119

Lin H. W., McDonald M., Benson B., Miller E., 2015, ApJ, 802,

34

Lin Y.-T., et al., 2017, ApJ, 851, 139

Lin Y.-T., Huang H.-J., Chen Y.-C., 2018, AJ, 155, 188

Machalski J., Godlowski W., 2000, A&A, 360, 463

Main R. A., McNamara B. R., Nulsen P. E. J., Russell H. R.,Vantyghem A. N., 2017, MNRAS, 464, 4360

Mamon G. A., Biviano A., Boue G., 2013, MNRAS, 429, 3079

Mauch T., Murphy T., Buttery H. J., Curran J., Hunstead R. W.,

Piestrzynski B., Robertson J. G., Sadler E. M., 2003, MNRAS,342, 1117

McAlpine K., Jarvis M. J., Bonfield D. G., 2013, MNRAS, 436,

1084

McClintock T., et al., 2019, MNRAS, 482, 1352

McDonald M., et al., 2012, Nature, 488, 349

McDonald M., et al., 2013, ApJ, 774, 23

McNamara B. R., Nulsen P. E. J., Wise M. W., Rafferty D. A.,

Carilli C., Sarazin C. L., Blanton E. L., 2005, Nature, 433, 45

McNamara B. R., et al., 2014, ApJ, 785, 44

Merloni A., et al., 2012, preprint, (arXiv:1209.3114)

Mills B. Y., 1981, Proceedings of the Astronomical Society ofAustralia, 4, 156

Mohr J. J., Evrard A. E., 1997, ApJ, 491, 38

Mohr J. J., Mathiesen B., Evrard A. E., 1999, ApJ, 517, 627

Morganson E., et al., 2018, PASP, 130, 074501

Mortonson M. J., Hu W., Huterer D., 2011, Phys. Rev. D, 83,

023015

Murphy T., Mauch T., Green A., Hunstead R. W., PiestrzynskaB., Kels A. P., Sztajer P., 2007, MNRAS, 382, 382

Navarro J. F., Frenk C. S., White S. D. M., 1997, ApJ, 490, 493

Ogrean G. A., Hatch N. A., Simionescu A., Bohringer H., BruggenM., Fabian A. C., Werner N., 2010, MNRAS, 406, 354

Panagoulia E. K., Fabian A. C., Sanders J. S., 2014, MNRAS,

438, 2341

Pracy M. B., et al., 2016, MNRAS, 460, 2

Predehl P., et al., 2010, in Society of Photo-Optical Instrumenta-

tion Engineers (SPIE) Conference Series. (arXiv:1001.2502),

doi:10.1117/12.856577

Rafferty D. A., McNamara B. R., Nulsen P. E. J., Wise M. W.,

2006, ApJ, 652, 216

Robertson J. G., 1991, Australian Journal of Physics, 44, 729

Rose T., et al., 2019, MNRAS, 485, 229

Rozo E., Rykoff E. S., 2014, ApJ, 783, 80

Rozo E., Rykoff E. S., Bartlett J. G., Evrard A., 2014a, MNRAS,

438, 49

Rozo E., Evrard A. E., Rykoff E. S., Bartlett J. G., 2014b, MN-

RAS, 438, 62

Rykoff E. S., et al., 2012, ApJ, 746, 178

Rykoff E. S., et al., 2014, ApJ, 785, 104

Rykoff E. S., et al., 2016, ApJS, 224, 1

Salpeter E. E., 1955, ApJ, 121, 161

Saro A., et al., 2015, MNRAS, 454, 2305

Sehgal N., Bode P., Das S., Hernandez-Monteagudo C., Huffen-

berger K., Lin Y., Ostriker J. P., Trac H., 2010, ApJ, 709,920

Semler D. R., et al., 2012, ApJ, 761, 183

Simpson C., Westoby P., Arumugam V., Ivison R., Hartley W.,Almaini O., 2013, MNRAS, 433, 2647

Smolcic V., et al., 2009, ApJ, 696, 24

Smolcic V., et al., 2017, A&A, 602, A6

Soergel B., et al., 2016, MNRAS, 461, 3172

Sommer M. W., Basu K., Pacaud F., Bertoldi F., Andernach H.,

2011, A&A, 529, A124

Stern C., et al., 2019, MNRAS, 485, 69

Stott J. P., et al., 2012, MNRAS, 422, 2213

Strazzullo V., Pannella M., Owen F. N., Bender R., Morrison

G. E., Wang W.-H., Shupe D. L., 2010, ApJ, 714, 1305

Sunyaev R. A., Zel’dovich Y. B., 1972, Comments on Astrophysics

and Space Physics, 4, 173

Temi P., Amblard A., Gitti M., Brighenti F., Gaspari M., Math-

ews W. G., David L., 2018, ApJ, 858, 17

Tremblay G. R., et al., 2016, Nature, 534, 218

Vantyghem A. N., et al., 2019, ApJ, 870, 57

Voit G. M., Donahue M., Bryan G. L., McDonald M., 2015, Na-

ture, 519, 203

Von Der Linden A., Best P. N., Kauffmann G., White S. D. M.,

2007, MNRAS, 379, 867

Webb T. M. A., et al., 2017, ApJ, 844, L17

Zhang Y., et al., 2016, ApJ, 816, 98

de Haan T., et al., 2016, ApJ, 832, 95

de Zotti G., Ricci R., Mesa D., Silva L., Mazzotta P., Toffolatti

L., Gonzalez-Nuevo J., 2005, A&A, 431, 893

AUTHOR AFFILIATIONS

1School of Physics, University of Melbourne, Parkville, VIC3010, Australia2Faculty of Physics, Ludwig-Maximilians-Universitat,Scheinerstr. 1, 81679 Munich, Germany3Excellence Cluster Origins, Boltzmannstr. 2, 85748 Garch-ing, Germany4Max Planck Institute for Extraterrestrial Physics, Giessen-bachstr. 85748 Garching, Germany5Kavli Institute for Particle Astrophysics & Cosmology,P. O. Box 2450, Stanford University, Stanford, CA 94305,USA6SLAC National Accelerator Laboratory, Menlo Park, CA

MNRAS 000, 000–000 (0000)

http://dx.doi.org/10.1086/670067

http://adsabs.harvard.edu/abs/2013PASP..125..306F

http://dx.doi.org/10.1088/0004-637X/694/2/1309

http://adsabs.harvard.edu/abs/2009ApJ...694.1309G

http://dx.doi.org/10.1155/2012/950641

http://dx.doi.org/10.1155/2012/950641

https://ui.adsabs.harvard.edu/#abs/2012AdAst2012E...6G

http://dx.doi.org/10.1093/mnras/stw1338

http://adsabs.harvard.edu/abs/2016MNRAS.461..560G


http://adsabs.harvard.edu/abs/2017MNRAS.467.3737G


http://adsabs.harvard.edu/abs/2017MNRAS.467.4015H

http://dx.doi.org/10.1111/j.1365-2966.2011.20405.x


http://dx.doi.org/10.1093/mnras/stt283

https://ui.adsabs.harvard.edu/#abs/2013MNRAS.431.1638H

http://dx.doi.org/10.1088/0004-637X/805/1/35

http://adsabs.harvard.edu/abs/2015ApJ...805...35H



http://dx.doi.org/10.1051/0004-6361/201219052

http://adsabs.harvard.edu/abs/2012A%26A...541A..62J

http://dx.doi.org/10.1111/j.1365-2966.2007.12752.x

http://adsabs.harvard.edu/abs/2008MNRAS.384..953K

http://adsabs.harvard.edu/abs/2008MNRAS.384..953K


http://adsabs.harvard.edu/abs/2018MNRAS.474.3324K


https://ui.adsabs.harvard.edu/abs/2019MNRAS.tmp.1397K

http://dx.doi.org/10.1134/S1063773717120015

https://ui.adsabs.harvard.edu/abs/2018AstL...44....8K

http://dx.doi.org/10.1088/0004-637X/700/1/221

http://esoads.eso.org/abs/2009ApJ...700..221K

http://dx.doi.org/10.1111/j.1365-2966.2012.21984.x

http://adsabs.harvard.edu/abs/2012MNRAS.427..550L


https://ui.adsabs.harvard.edu/#abs/2013MNRAS.433..825L

http://dx.doi.org/10.1086/425412

http://adsabs.harvard.edu/abs/2004ApJ...617..879L

http://dx.doi.org/10.1086/513565

http://adsabs.harvard.edu/abs/2007ApJS..170...71L

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2004ApJ...610..745L&db_key=AST

http://dx.doi.org/10.1088/0004-637X/694/2/992



http://dx.doi.org/10.1088/0004-637X/723/2/1119

http://adsabs.harvard.edu/abs/2010ApJ...723.1119L

http://dx.doi.org/10.1088/0004-637X/802/1/34

http://adsabs.harvard.edu/abs/2015ApJ...802...34L

http://adsabs.harvard.edu/abs/2015ApJ...802...34L

http://dx.doi.org/10.3847/1538-4357/aa9bf5


http://dx.doi.org/10.3847/1538-3881/aab5b4

http://adsabs.harvard.edu/abs/2018AJ....155..188L

http://adsabs.harvard.edu/abs/2000A%26A...360..463M


https://ui.adsabs.harvard.edu/abs/2017MNRAS.464.4360M

http://dx.doi.org/10.1093/mnras/sts565

http://adsabs.harvard.edu/abs/2013MNRAS.429.3079M





https://ui.adsabs.harvard.edu/abs/2019MNRAS.482.1352M

http://dx.doi.org/10.1038/nature11379

http://adsabs.harvard.edu/abs/2012arXiv1208.2962M

http://dx.doi.org/10.1088/0004-637X/774/1/23

http://adsabs.harvard.edu/abs/2013ApJ...774...23M


http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005Natur.433...45M&db_key=AST

http://dx.doi.org/10.1088/0004-637X/785/1/44

https://ui.adsabs.harvard.edu/#abs/2014ApJ...785...44M

http://arxiv.org/abs/1209.3114

http://adsabs.harvard.edu/abs/1981PASAu...4..156M

http://dx.doi.org/10.1086/304957

https://ui.adsabs.harvard.edu/abs/1997ApJ...491...38M

http://dx.doi.org/10.1086/307227

https://ui.adsabs.harvard.edu/abs/1999ApJ...517..627M

http://dx.doi.org/10.1088/1538-3873/aab4ef

http://adsabs.harvard.edu/abs/2018PASP..130g4501M

http://dx.doi.org/10.1103/PhysRevD.83.023015

http://adsabs.harvard.edu/abs/2011PhRvD..83b3015M

http://adsabs.harvard.edu/abs/2011PhRvD..83b3015M

http://dx.doi.org/10.1111/j.1365-2966.2007.12379.x

http://adsabs.harvard.edu/abs/2007MNRAS.382..382M

http://dx.doi.org/10.1086/304888

http://adsabs.harvard.edu/abs/1997ApJ...490..493N

http://dx.doi.org/10.1111/j.1365-2966.2010.16718.x

https://ui.adsabs.harvard.edu/#abs/2010MNRAS.406..354O


https://ui.adsabs.harvard.edu/abs/2014MNRAS.438.2341P


http://adsabs.harvard.edu/abs/2016MNRAS.460....2P

http://arxiv.org/abs/1001.2502

http://dx.doi.org/10.1117/12.856577

http://dx.doi.org/10.1086/507672

http://adsabs.harvard.edu/abs/2006ApJ...652..216R

http://adsabs.harvard.edu/abs/1991AuJPh..44..729R


https://ui.adsabs.harvard.edu/#abs/2019MNRAS.485..229R

http://dx.doi.org/10.1088/0004-637X/783/2/80

http://adsabs.harvard.edu/abs/2014ApJ...783...80R


http://adsabs.harvard.edu/abs/2014MNRAS.438...49R



http://adsabs.harvard.edu/abs/2014MNRAS.438...62R

http://dx.doi.org/10.1088/0004-637X/746/2/178


http://dx.doi.org/10.1088/0004-637X/785/2/104


http://dx.doi.org/10.3847/0067-0049/224/1/1

http://adsabs.harvard.edu/abs/2016ApJS..224....1R

http://dx.doi.org/10.1086/145971

http://adsabs.harvard.edu/abs/1955ApJ...121..161S


http://adsabs.harvard.edu/abs/2015MNRAS.454.2305S

http://dx.doi.org/10.1088/0004-637X/709/2/920



http://dx.doi.org/10.1088/0004-637X/761/2/183




http://dx.doi.org/10.1088/0004-637X/696/1/24

http://esoads.eso.org/abs/2009ApJ...696...24S

http://dx.doi.org/10.1051/0004-6361/201730685

https://ui.adsabs.harvard.edu/abs/2017A%26A...602A...6S



http://dx.doi.org/10.1051/0004-6361/201016150

http://adsabs.harvard.edu/abs/2011A%26A...529A.124S


http://adsabs.harvard.edu/abs/2019MNRAS.485...69S

http://dx.doi.org/10.1111/j.1365-2966.2012.20764.x


http://dx.doi.org/10.1088/0004-637X/714/2/1305

http://adsabs.harvard.edu/abs/2010ApJ...714.1305S

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1972CoASP...4..173S&db_key=AST

http://dx.doi.org/10.3847/1538-4357/aab9b0

https://ui.adsabs.harvard.edu/#abs/2018ApJ...858...17T


http://adsabs.harvard.edu/abs/2016Natur.534..218T

http://dx.doi.org/10.3847/1538-4357/aaf1b4

https://ui.adsabs.harvard.edu/#abs/2019ApJ...870...57V



http://adsabs.harvard.edu/abs/2015Natur.519..203V

http://dx.doi.org/10.1111/j.1365-2966.2007.11940.x

https://ui.adsabs.harvard.edu/abs/2007MNRAS.379..867V

http://dx.doi.org/10.3847/2041-8213/aa7749

https://ui.adsabs.harvard.edu/#abs/2017ApJ...844L..17W

http://dx.doi.org/10.3847/0004-637X/816/2/98

https://ui.adsabs.harvard.edu/abs/2016ApJ...816...98Z

http://dx.doi.org/10.3847/0004-637X/832/1/95


http://dx.doi.org/10.1051/0004-6361:20042108

http://adsabs.harvard.edu/abs/2005A%26A...431..893D


94025, USA7Fermi National Accelerator Laboratory, P. O. Box 500,Batavia, IL 60510, USA8Instituto de Fisica Teorica UAM/CSIC, UniversidadAutonoma de Madrid, 28049 Madrid, Spain9Department of Physics & Astronomy, University CollegeLondon, Gower Street, London, WC1E 6BT, UK10Center for Astrophysics | Harvard & Smithsonian, 60Garden Street, Cambridge, MA 02138, USA11Kavli Institute for Astrophysics and Space Research,Massachusetts Institute of Technology, 77 MassachusettsAvenue, Cambridge, MA 0213912Centro de Investigaciones Energeticas, Medioambientalesy Tecnologicas (CIEMAT), Madrid, Spain13Laboratorio Interinstitucional de e-Astronomia - LIneA,Rua Gal. Jose Cristino 77, Rio de Janeiro, RJ - 20921-400,Brazil14Department of Astronomy, University of Illinois atUrbana-Champaign, 1002 W. Green Street, Urbana, IL61801, USA15National Center for Supercomputing Applications, 1205West Clark St., Urbana, IL 61801, USA16Institut de Fısica d’Altes Energies (IFAE), The BarcelonaInstitute of Science and Technology, Campus UAB, 08193Bellaterra (Barcelona) Spain17Academia Sinica Institute of Astronomy and Astrophysics,11F of AS/NTU Astronomy-Mathematics Building, No.1,Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan18Observatorio Nacional, Rua Gal. Jose Cristino 77, Rio deJaneiro, RJ - 20921-400, Brazil19Department of Physics, IIT Hyderabad, Kandi, Telangana502285, India20Santa Cruz Institute for Particle Physics, Santa Cruz, CA95064, USA21Department of Astronomy, University of Michigan, AnnArbor, MI 48109, USA22Department of Physics, University of Michigan, AnnArbor, MI 48109, USA23Institut d’Estudis Espacials de Catalunya (IEEC), 08034Barcelona, Spain24Institute of Space Sciences (ICE, CSIC), Campus UAB,Carrer de Can Magrans, s/n, 08193 Barcelona, Spain25Department of Physics, Stanford University, 382 ViaPueblo Mall, Stanford, CA 94305, USA26Department of Physics, The Ohio State University,Columbus, OH 43210, USA27Australian Astronomical Optics, Macquarie University,North Ryde, NSW 2113, Australia28The Research School of Astronomy and Astrophysics,Australian National University, ACT 2601, Australia29Departamento de Fısica Matematica, Instituto de Fısica,Universidade de Sao Paulo, CP 66318, Sao Paulo, SP,05314-970, Brazil30George P. and Cynthia Woods Mitchell Institute forFundamental Physics and Astronomy, and Department ofPhysics and Astronomy, Texas A&M University, CollegeStation, TX 77843, USA31Institucio Catalana de Recerca i Estudis Avancats,E-08010 Barcelona, Spain32Department of Astrophysical Sciences, Princeton Univer-sity, Peyton Hall, Princeton, NJ 08544, USA33Instituto de Fısica, UFRGS, Caixa Postal 15051, Porto

Alegre, RS - 91501-970, Brazil34INAF-Osservatorio Astronomico di Trieste, via Tiepolo11, I-34143 Trieste, Italy35IFPU - Institute for Fundamental Physics of the Universe,Via Beirut 2, 34014 Trieste, Italy36INAF-Osservatorio Astronomico di Trieste, via G. B.Tiepolo 11, I-34143 Trieste, Italy37School of Physics and Astronomy, University of Southamp-ton, Southampton, SO17 1BJ, UK38Department of Physics, Lancaster University, Lancaster,LA1 4YB, UK39Computer Science and Mathematics Division, Oak RidgeNational Laboratory, Oak Ridge, TN 3783140Argonne National Laboratory, 9700 South Cass Avenue,Lemont, IL 60439, USA41Cerro Tololo Inter-American Observatory, Casilla 603, LaSerena, Chile

MNRAS 000, 000–000 (0000)

Documents

Constraining Radio Mode Feedback in Galaxy Clusters with